Operator Algebras And K Theory

Author : Bruce Blackadar
Publisher : Springer Science & Business Media
Page : 347 pages
File Size : 53,7 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.

Author : M. Rørdam,Flemming Larsen,N. Laustsen
Publisher : Cambridge University Press
Page : 260 pages
File Size : 45,9 Mb
Release : 2000-07-20
Category : Mathematics
ISBN : 0521789443

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An Introduction to K-Theory for C*-Algebras by M. Rørdam,Flemming Larsen,N. Laustsen Pdf

This book provides a very elementary introduction to K-theory for C*-algebras, and is ideal for beginning graduate students.

Author : Ronald G. Douglas,Claude Schochet
Publisher : American Mathematical Soc.
Page : 204 pages
File Size : 51,9 Mb
Release : 1982
Category : Mathematics
ISBN : 9780821850114

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Operator Algebras and $K$-Theory by Ronald G. Douglas,Claude Schochet Pdf

Author : Bruce Blackadar
Publisher : Springer Science & Business Media
Page : 528 pages
File Size : 48,8 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.

Author : David E. Evans,Masamichi Takesaki
Publisher : Cambridge University Press
Page : 257 pages
File Size : 43,5 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.

Author : Alain Connes,Joachim Cuntz,Erik G. Guentner,Nigel Higson,Jerome Kaminker,John E. Roberts
Publisher : Springer Science & Business Media
Page : 372 pages
File Size : 40,5 Mb
Release : 2003-12-08
Category : Mathematics
ISBN : 3540203575

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Noncommutative Geometry by Alain Connes,Joachim Cuntz,Erik G. Guentner,Nigel Higson,Jerome Kaminker,John E. Roberts Pdf

Noncommutative Geometry is one of the most deep and vital research subjects of present-day Mathematics. Its development, mainly due to Alain Connes, is providing an increasing number of applications and deeper insights for instance in Foliations, K-Theory, Index Theory, Number Theory but also in Quantum Physics of elementary particles. The purpose of the Summer School in Martina Franca was to offer a fresh invitation to the subject and closely related topics; the contributions in this volume include the four main lectures, cover advanced developments and are delivered by prominent specialists.

Author : Gerald J. Murphy
Publisher : Academic Press
Page : 296 pages
File Size : 46,7 Mb
Release : 2014-06-28
Category : Mathematics
ISBN : 9780080924960

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C*-Algebras and Operator Theory by Gerald J. Murphy Pdf

This book constitutes a first- or second-year graduate course in operator theory. It is a field that has great importance for other areas of mathematics and physics, such as algebraic topology, differential geometry, and quantum mechanics. It assumes a basic knowledge in functional analysis but no prior acquaintance with operator theory is required.

Author : Joachim Cuntz,Siegfried Echterhoff,Xin Li,Guoliang Yu
Publisher : Birkhäuser
Page : 322 pages
File Size : 54,7 Mb
Release : 2017-10-24
Category : Mathematics
ISBN : 9783319599151

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K-Theory for Group C*-Algebras and Semigroup C*-Algebras by Joachim Cuntz,Siegfried Echterhoff,Xin Li,Guoliang Yu Pdf

This book gives an account of the necessary background for group algebras and crossed products for actions of a group or a semigroup on a space and reports on some very recently developed techniques with applications to particular examples. Much of the material is available here for the first time in book form. The topics discussed are among the most classical and intensely studied C*-algebras. They are important for applications in fields as diverse as the theory of unitary group representations, index theory, the topology of manifolds or ergodic theory of group actions. Part of the most basic structural information for such a C*-algebra is contained in its K-theory. The determination of the K-groups of C*-algebras constructed from group or semigroup actions is a particularly challenging problem. Paul Baum and Alain Connes proposed a formula for the K-theory of the reduced crossed product for a group action that would permit, in principle, its computation. By work of many hands, the formula has by now been verified for very large classes of groups and this work has led to the development of a host of new techniques. An important ingredient is Kasparov's bivariant K-theory. More recently, also the C*-algebras generated by the regular representation of a semigroup as well as the crossed products for actions of semigroups by endomorphisms have been studied in more detail. Intriguing examples of actions of such semigroups come from ergodic theory as well as from algebraic number theory. The computation of the K-theory of the corresponding crossed products needs new techniques. In cases of interest the K-theory of the algebras reflects ergodic theoretic or number theoretic properties of the action.

Author : B.B. Morrel,I.M. Singer
Publisher : Springer
Page : 200 pages
File Size : 49,5 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540374237

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K-Theory and Operator Algebras by B.B. Morrel,I.M. Singer Pdf

Author : M. Rordam,E. Stormer
Publisher : Springer Science & Business Media
Page : 206 pages
File Size : 41,7 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.

Author : Herbert Schröder
Publisher : Chapman and Hall/CRC
Page : 184 pages
File Size : 53,7 Mb
Release : 1993-08-23
Category : Mathematics
ISBN : UOM:39015029969386

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K-Theory for Real C*-Algebras and Applications by Herbert Schröder Pdf

This Research Note presents the K-theory and KK-theory for real C*-algebras and shows that these can be successfully applied to solve some topological problems which are not accessible to the tools developed in the complex setting alone.

Author : Liming Ge
Publisher : American Mathematical Soc.
Page : 389 pages
File Size : 40,6 Mb
Release : 1998
Category : Mathematics
ISBN : 9780821810934

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Operator Algebras and Operator Theory by Liming Ge Pdf

This volume contains the proceedings from the International Conference on Operator Algebras and Operator Theory held at the East China Normal University in Shanghai (China). Participants in the conference ranged from graduate students to postdocs to leading experts who came from around the world. Topics covered in this title were $C^*$-algebras, von Neumann algebras, non-self-adjoint operator algebras, wavelets, operator spaces and other related areas. This work consists of contributions from invited speakers and some mathematicians who were unable to attend. It presents important mathematical ideas while maintaining the uniqueness and excitement of this very successful event.

Author : Niels Erik Wegge-Olsen
Publisher : Oxford University Press on Demand
Page : 370 pages
File Size : 49,6 Mb
Release : 1993
Category : Mathematics
ISBN : 0198596944

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K-theory and C*-algebras by Niels Erik Wegge-Olsen Pdf

K-theory is often considered a complicated mathematical theory for specialists only. This book is an accessible introduction to the basics and provides detailed explanations of the various concepts required for a deeper understanding of the subject. Some familiarity with basic C*algebra theory is assumed. The book then follows a careful construction and analysis of the operator K-theory groups and proof of the results of K-theory, including Bott periodicity. Of specific interest to algebraists and geometrists, the book aims to give full instruction. No details are left out in the presentation and many instructive and generously hinted exercises are provided. Apart from K-theory, this book offers complete and self contained expositions of important advanced C*-algebraic constructions like tensor products, multiplier algebras and Hilbert modules.

Author : M. Takesaki
Publisher : Springer Science & Business Media
Page : 444 pages
File Size : 42,5 Mb
Release : 2001-11-20
Category : Mathematics
ISBN : 354042248X

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Theory of Operator Algebras I by M. Takesaki Pdf

Since its inception by von Neumann 70 years ago, the theory of operator algebras has become a rapidly developing area of importance for the understanding of many areas of mathematics and theoretical physics. Accessible to the non-specialist, this first part of a three-volume treatise provides a clear, carefully written survey that emphasizes the theory's analytical and topological aspects.

Author : Joachim Cuntz,Jonathan Rosenberg
Publisher : Springer Science & Business Media
Page : 268 pages
File Size : 42,8 Mb
Release : 2007-07-19
Category : Mathematics
ISBN : 9783764383985

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Topological and Bivariant K-Theory by Joachim Cuntz,Jonathan Rosenberg Pdf

Topological K-theory is one of the most important invariants for noncommutative algebras. Bott periodicity, homotopy invariance, and various long exact sequences distinguish it from algebraic K-theory. This book describes a bivariant K-theory for bornological algebras, which provides a vast generalization of topological K-theory. In addition, it details other approaches to bivariant K-theories for operator algebras. The book studies a number of applications, including K-theory of crossed products, the Baum-Connes assembly map, twisted K-theory with some of its applications, and some variants of the Atiyah-Singer Index Theorem.