Operator Algebras And Geometry

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Operator Algebras and Geometry

Hitoshi Moriyoshi,Toshikazu Natsume
Operator Algebras and Geometry Book PDF

Author : Hitoshi Moriyoshi,Toshikazu Natsume
Publisher : American Mathematical Soc.
Page : 155 pages
File Size : 47,9 Mb
Release : 2008
Category : Mathematics
ISBN : 0821839470

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Operator Algebras and Geometry by Hitoshi Moriyoshi,Toshikazu Natsume Pdf

In the early 1980's topologists and geometers for the first time came across unfamiliar words like $C^*$-algebras and von Neumann algebras through the discovery of new knot invariants (by V. F. R. Jones) or through a remarkable result on the relationship between characteristic classes of foliations and the types of certain von Neumann algebras. During the following two decades, a great deal of progress was achieved in studying the interaction between geometry and analysis, in particular in noncommutative geometry and mathematical physics. The present book provides an overview of operator algebra theory and an introduction to basic tools used in noncommutative geometry. The book concludes with applications of operator algebras to Atiyah-Singer type index theorems. The purpose of the book is to convey an outline and general idea of operator algebra theory, to some extent focusing on examples. The book is aimed at researchers and graduate students working in differential topology, differential geometry, and global analysis who are interested in learning about operator algebras.

Geometry of State Spaces of Operator Algebras

Erik M. Alfsen,Frederic W. Shultz
Geometry of State Spaces of Operator Algebras Book PDF

Author : Erik M. Alfsen,Frederic W. Shultz
Publisher : Springer Science & Business Media
Page : 467 pages
File Size : 49,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461200192

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Geometry of State Spaces of Operator Algebras by Erik M. Alfsen,Frederic W. Shultz Pdf

In this book we give a complete geometric description of state spaces of operator algebras, Jordan as well as associative. That is, we give axiomatic characterizations of those convex sets that are state spaces of C*-algebras and von Neumann algebras, together with such characterizations for the normed Jordan algebras called JB-algebras and JBW-algebras. These non associative algebras generalize C*-algebras and von Neumann algebras re spectively, and the characterization of their state spaces is not only of interest in itself, but is also an important intermediate step towards the characterization of the state spaces of the associative algebras. This book gives a complete and updated presentation of the character ization theorems of [10]' [11] and [71]. Our previous book State spaces of operator algebras: basic theory, orientations and C*-products, referenced as [AS] in the sequel, gives an account of the necessary prerequisites on C*-algebras and von Neumann algebras, as well as a discussion of the key notion of orientations of state spaces. For the convenience of the reader, we have summarized these prerequisites in an appendix which contains all relevant definitions and results (listed as (AI), (A2), ... ), with reference back to [AS] for proofs, so that this book is self-contained.

Operator Algebras and Applications: Volume 1, Structure Theory; K-theory, Geometry and Topology

David E. Evans,Masamichi Takesaki
Operator Algebras and Applications Volume 1 Structure Theory K theory Geometry and Topology Book PDF

Author : David E. Evans,Masamichi Takesaki
Publisher : Cambridge University Press
Page : 257 pages
File Size : 42,7 Mb
Release : 1988
Category : Mathematics
ISBN : 9780521368438

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Operator Algebras and Applications: Volume 1, Structure Theory; K-theory, Geometry and Topology by David E. Evans,Masamichi Takesaki Pdf

These volumes form an authoritative statement of the current state of research in Operator Algebras. They consist of papers arising from a year-long symposium held at the University of Warwick. Contributors include many very well-known figures in the field.

Operator Theory, Operator Algebras and Their Interactions with Geometry and Topology

Raul E Curto,William Helton,Huaxin Lin,Xiang Tang,Rongwei Yang,Guoliang Yu
Operator Theory Operator Algebras and Their Interactions with Geometry and Topology Book PDF

Author : Raul E Curto,William Helton,Huaxin Lin,Xiang Tang,Rongwei Yang,Guoliang Yu
Publisher : Springer Nature
Page : 531 pages
File Size : 40,6 Mb
Release : 2020-12-12
Category : Mathematics
ISBN : 9783030433802

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Operator Theory, Operator Algebras and Their Interactions with Geometry and Topology by Raul E Curto,William Helton,Huaxin Lin,Xiang Tang,Rongwei Yang,Guoliang Yu Pdf

This book is the proceeding of the International Workshop on Operator Theory and Applications (IWOTA) held in July 2018 in Shanghai, China. It consists of original papers, surveys and expository articles in the broad areas of operator theory, operator algebras and noncommutative topology. Its goal is to give graduate students and researchers a relatively comprehensive overview of the current status of research in the relevant fields. The book is also a special volume dedicated to the memory of Ronald G. Douglas who passed away on February 27, 2018 at the age of 79. Many of the contributors are Douglas’ students and past collaborators. Their articles attest and commemorate his life-long contribution and influence to these fields.

Operator Algebras, Quantization, and Noncommutative Geometry

Marshall Harvey Stone,Robert S. Doran,Richard V. Kadison
Operator Algebras Quantization and Noncommutative Geometry Book PDF

Author : Marshall Harvey Stone,Robert S. Doran,Richard V. Kadison
Publisher : American Mathematical Soc.
Page : 422 pages
File Size : 49,6 Mb
Release : 2004
Category : Mathematics
ISBN : 9780821834022

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Operator Algebras, Quantization, and Noncommutative Geometry by Marshall Harvey Stone,Robert S. Doran,Richard V. Kadison Pdf

John von Neumann and Marshall Stone were two giants of Twentieth Century mathematics. In honor of the 100th anniversary of their births, a mathematical celebration was organized featuring developments in fields where both men were major influences. This volume contains articles from the AMS Special Session, Operator Algebras, Quantization and Noncommutative Geometry: A Centennial Celebration in Honor of John von Neumann and Marshall H. Stone.Papers range from expository and historical surveys to original research articles. All articles were carefully refereed and cover a broad range of mathematical topics reflecting the fundamental ideas of von Neumann and Stone. Most contributions are expanded versions of the talks and were written exclusively for this volume. Included, among others, are articles by George W. Mackey, Nigel Higson, and Marc Rieffel. Also featured is a reprint of P.R. Halmos' ""The Legend of John von Neumann"". The book is suitable for graduate students and researchers interested in operator algebras and applications, including noncommutative geometry.

Two-Dimensional Conformal Geometry and Vertex Operator Algebras

Yi-Zhi Huang
Two Dimensional Conformal Geometry and Vertex Operator Algebras Book PDF

Author : Yi-Zhi Huang
Publisher : Springer Science & Business Media
Page : 289 pages
File Size : 54,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461242765

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Two-Dimensional Conformal Geometry and Vertex Operator Algebras by Yi-Zhi Huang Pdf

The theory of vertex operator algebras and their representations has been showing its power in the solution of concrete mathematical problems and in the understanding of conceptual but subtle mathematical and physical struc- tures of conformal field theories. Much of the recent progress has deep connec- tions with complex analysis and conformal geometry. Future developments, especially constructions and studies of higher-genus theories, will need a solid geometric theory of vertex operator algebras. Back in 1986, Manin already observed in Man) that the quantum theory of (super )strings existed (in some sense) in two entirely different mathematical fields. Under canonical quantization this theory appeared to a mathematician as the representation theories of the Heisenberg, Vir as oro and affine Kac- Moody algebras and their superextensions. Quantization with the help of the Polyakov path integral led on the other hand to the analytic theory of algebraic (super ) curves and their moduli spaces, to invariants of the type of the analytic curvature, and so on.He pointed out further that establishing direct mathematical connections between these two forms of a single theory was a big and important problem. On the one hand, the theory of vertex operator algebras and their repre- sentations unifies (and considerably extends) the representation theories of the Heisenberg, Virasoro and Kac-Moody algebras and their superextensions.

Theory of Operator Algebras I

Masamichi Takesaki
Theory of Operator Algebras I Book PDF

Author : Masamichi Takesaki
Publisher : Springer Science & Business Media
Page : 424 pages
File Size : 51,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461261889

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Theory of Operator Algebras I by Masamichi Takesaki Pdf

Mathematics for infinite dimensional objects is becoming more and more important today both in theory and application. Rings of operators, renamed von Neumann algebras by J. Dixmier, were first introduced by J. von Neumann fifty years ago, 1929, in [254] with his grand aim of giving a sound founda tion to mathematical sciences of infinite nature. J. von Neumann and his collaborator F. J. Murray laid down the foundation for this new field of mathematics, operator algebras, in a series of papers, [240], [241], [242], [257] and [259], during the period of the 1930s and early in the 1940s. In the introduction to this series of investigations, they stated Their solution 1 {to the problems of understanding rings of operators) seems to be essential for the further advance of abstract operator theory in Hilbert space under several aspects. First, the formal calculus with operator-rings leads to them. Second, our attempts to generalize the theory of unitary group-representations essentially beyond their classical frame have always been blocked by the unsolved questions connected with these problems. Third, various aspects of the quantum mechanical formalism suggest strongly the elucidation of this subject. Fourth, the knowledge obtained in these investigations gives an approach to a class of abstract algebras without a finite basis, which seems to differ essentially from all types hitherto investigated. Since then there has appeared a large volume of literature, and a great deal of progress has been achieved by many mathematicians.

Operator Algebras

Bruce Blackadar
Operator Algebras Book PDF

Author : Bruce Blackadar
Publisher : Springer Science & Business Media
Page : 528 pages
File Size : 46,6 Mb
Release : 2006-03-09
Category : Mathematics
ISBN : 9783540285175

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Operator Algebras by Bruce Blackadar Pdf

This book offers a comprehensive introduction to the general theory of C*-algebras and von Neumann algebras. Beginning with the basics, the theory is developed through such topics as tensor products, nuclearity and exactness, crossed products, K-theory, and quasidiagonality. The presentation carefully and precisely explains the main features of each part of the theory of operator algebras; most important arguments are at least outlined and many are presented in full detail.

Recent Advances in Operator Theory and Operator Algebras

Hari Bercovici,Elias Katsoulis,David Kerr,Dan Timotin
Recent Advances in Operator Theory and Operator Algebras Book PDF

Author : Hari Bercovici,Elias Katsoulis,David Kerr,Dan Timotin
Publisher : CRC Press
Page : 167 pages
File Size : 40,8 Mb
Release : 2017-08-07
Category : Mathematics
ISBN : 9781317974611

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Recent Advances in Operator Theory and Operator Algebras by Hari Bercovici,Elias Katsoulis,David Kerr,Dan Timotin Pdf

This book will contain lectures given by four eminent speakers at the Recent Advances in Operator Theory and Operator Algebras conference held at the Indian Statistical Institute, Bangalore, India in 2014. The main aim of this book is to bring together various results in one place with cogent introduction and references for further study.

Operator Algebras

Bruce Blackadar
Operator Algebras Book PDF

Author : Bruce Blackadar
Publisher : Unknown
Page : 517 pages
File Size : 40,5 Mb
Release : 2006-01-01
Category : C*-algebras
ISBN : 6610462127

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Operator Algebras by Bruce Blackadar Pdf

This book is the most comprehensive treatment available of the general theory of C*-algebras and von Neumann algebras. Beginning with the basics, the theory is developed through such topics as tensor products, nuclearity and exactness, crossed products, classification of injective factors, K-theory, finiteness, stable rank, and quasidiagonality. The presentation concentrates on carefully and precisely explaining the main features of each part of the theory of operator algebras; most important arguments are at least outlined, and many are presented in full detail, so the volume is much more than a mere survey.

State Spaces of Operator Algebras

Erik M. Alfsen,Frederik W. Shultz
State Spaces of Operator Algebras Book PDF

Author : Erik M. Alfsen,Frederik W. Shultz
Publisher : Springer Science & Business Media
Page : 372 pages
File Size : 55,5 Mb
Release : 2001-04-27
Category : Mathematics
ISBN : 0817638903

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State Spaces of Operator Algebras by Erik M. Alfsen,Frederik W. Shultz Pdf

The topic of this book is the theory of state spaces of operator algebras and their geometry. The states are of interest because they determine representations of the algebra, and its algebraic structure is in an intriguing and fascinating fashion encoded in the geometry of the state space. From the beginning the theory of operator algebras was motivated by applications to physics, but recently it has found unexpected new applica tions to various fields of pure mathematics, like foliations and knot theory, and (in the Jordan algebra case) also to Banach manifolds and infinite di mensional holomorphy. This makes it a relevant field of study for readers with diverse backgrounds and interests. Therefore this book is not intended solely for specialists in operator algebras, but also for graduate students and mathematicians in other fields who want to learn the subject. We assume that the reader starts out with only the basic knowledge taught in standard graduate courses in real and complex variables, measure theory and functional analysis. We have given complete proofs of basic results on operator algebras, so that no previous knowledge in this field is needed. For discussion of some topics, more advanced prerequisites are needed. Here we have included all necessary definitions and statements of results, but in some cases proofs are referred to standard texts. In those cases we have tried to give references to material that can be read and understood easily in the context of our book.

Classification of Nuclear C*-Algebras. Entropy in Operator Algebras

M. Rordam,E. Stormer
Classification of Nuclear C Algebras Entropy in Operator Algebras Book PDF

Author : M. Rordam,E. Stormer
Publisher : Springer Science & Business Media
Page : 206 pages
File Size : 42,8 Mb
Release : 2013-04-18
Category : Mathematics
ISBN : 9783662048252

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Classification of Nuclear C*-Algebras. Entropy in Operator Algebras by M. Rordam,E. Stormer Pdf

to the Encyclopaedia Subseries on Operator Algebras and Non-Commutative Geometry The theory of von Neumann algebras was initiated in a series of papers by Murray and von Neumann in the 1930's and 1940's. A von Neumann algebra is a self-adjoint unital subalgebra M of the algebra of bounded operators of a Hilbert space which is closed in the weak operator topology. According to von Neumann's bicommutant theorem, M is closed in the weak operator topology if and only if it is equal to the commutant of its commutant. Afactor is a von Neumann algebra with trivial centre and the work of Murray and von Neumann contained a reduction of all von Neumann algebras to factors and a classification of factors into types I, II and III. C* -algebras are self-adjoint operator algebras on Hilbert space which are closed in the norm topology. Their study was begun in the work of Gelfand and Naimark who showed that such algebras can be characterized abstractly as involutive Banach algebras, satisfying an algebraic relation connecting the norm and the involution. They also obtained the fundamental result that a commutative unital C* -algebra is isomorphic to the algebra of complex valued continuous functions on a compact space - its spectrum. Since then the subject of operator algebras has evolved into a huge mathematical endeavour interacting with almost every branch of mathematics and several areas of theoretical physics.

Theory of Operator Algebras II

Masamichi Takesaki
Theory of Operator Algebras II Book PDF

Author : Masamichi Takesaki
Publisher : Springer Science & Business Media
Page : 552 pages
File Size : 52,7 Mb
Release : 2002-11-01
Category : Mathematics
ISBN : 354042914X

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Theory of Operator Algebras II by Masamichi Takesaki Pdf

Together with Theory of Operator Algebras I and III, this book presents the theory of von Neumann algebras and non-commutative integration focusing on the group of automorphisms and the structure analysis. From the reviews: "These books can be warmly recommended to every graduate student who wants to become acquainted with this exciting branch of mathematics. Furthermore, they should be on the bookshelf of every researcher of the area." --ACTA SCIENTIARUM MATHEMATICARUM

K-Theory for Operator Algebras

Bruce Blackadar
K Theory for Operator Algebras Book PDF

Author : Bruce Blackadar
Publisher : Springer Science & Business Media
Page : 347 pages
File Size : 55,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461395720

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K-Theory for Operator Algebras by Bruce Blackadar Pdf

K -Theory has revolutionized the study of operator algebras in the last few years. As the primary component of the subject of "noncommutative topol ogy," K -theory has opened vast new vistas within the structure theory of C* algebras, as well as leading to profound and unexpected applications of opera tor algebras to problems in geometry and topology. As a result, many topolo gists and operator algebraists have feverishly begun trying to learn each others' subjects, and it appears certain that these two branches of mathematics have become deeply and permanently intertwined. Despite the fact that the whole subject is only about a decade old, operator K -theory has now reached a state of relative stability. While there will undoubtedly be many more revolutionary developments and applications in the future, it appears the basic theory has more or less reached a "final form." But because of the newness of the theory, there has so far been no comprehensive treatment of the subject. It is the ambitious goal of these notes to fill this gap. We will develop the K -theory of Banach algebras, the theory of extensions of C*-algebras, and the operator K -theory of Kasparov from scratch to its most advanced aspects. We will not treat applications in detail; however, we will outline the most striking of the applications to date in a section at the end, as well as mentioning others at suitable points in the text.

Index Theory and Operator Algebras

Jeffrey Stephen Fox,Peter Haskell
Index Theory and Operator Algebras Book PDF

Author : Jeffrey Stephen Fox,Peter Haskell
Publisher : American Mathematical Soc.
Page : 190 pages
File Size : 50,9 Mb
Release : 1993
Category : Mathematics
ISBN : 9780821851524

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Index Theory and Operator Algebras by Jeffrey Stephen Fox,Peter Haskell Pdf

This collection of papers by leading researchers provides a broad picture of current research directions in index theory. Based on lectures presented at the NSF-CBMS Regional Conference on K-Homology and Index Theory, held in August 1991 at the University of Colorado at Boulder, the book provides both a careful exposition of new perspectives in classical index theory and an introduction to currently active areas of the field. Presented here are two new proofs of the classical Atiyah-Singer Index Theorem, as well as index theorems for manifolds with boundary and open manifolds. Index theory for semi-simple p-adic groups and the geometry of discrete groups are also discussed. Through-out the book, the application of operator algebras emerges as a central theme. Aimed at graduate students and researchers, this book would be suitable as a text for an advanced graduate topics course on index theory.