Fundamentals Of The Theory Of Operator Algebras

Author : Richard V. Kadison,John R. Ringrose
Publisher : American Mathematical Soc.
Page : 290 pages
File Size : 46,5 Mb
Release : 1998-01-13
Category : Mathematics
ISBN : 9780821894699

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Fundamentals of the Theory of Operator Algebras. Volume III by Richard V. Kadison,John R. Ringrose Pdf

This volume is the companion volume to Fundamentals of the Theory of Operator Algebras. Volume I--Elementary Theory (Graduate Studies in Mathematics series, Volume 15). The goal of the text proper is to teach the subject and lead readers to where the vast literature--in the subject specifically and in its many applications--becomes accessible. The choice of material was made from among the fundamentals of what may be called the "classical" theory of operator algebras. This volume contains the written solutions to the exercises in the Fundamentals of the Theory of Operator Algebras. Volume I--Elementary Theory.

Author : Richard V. Kadison, John R. Ringrose
Publisher : American Mathematical Soc.
Page : 604 pages
File Size : 52,8 Mb
Release : 1998-01-13
Category : Mathematics
ISBN : 9780821894682

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Fundamentals of the Theory of Operator Algebras. Volume IV by Richard V. Kadison, John R. Ringrose Pdf

This volume is the companion volume to Fundamentals of the Theory of Operator Algebras. Volume II--Advanced Theory (Graduate Studies in Mathematics series, Volume 16). The goal of the text proper is to teach the subject and lead readers to where the vast literature--in the subject specifically and in its many applications--becomes accessible. The choice of material was made from among the fundamentals of what may be called the "classical" theory of operator algebras. This volume contains the written solutions to the exercises in the Fundamentals of the Theory of Operator Algebras. Volume II--Advanced Theory.

Author : KADISON,RINGROSE
Publisher : Springer Science & Business Media
Page : 599 pages
File Size : 55,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461229681

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Fundamentals of the Theory of Operator Algebras by KADISON,RINGROSE Pdf

These volumes are companions to the treatise; "Fundamentals of the Theory of Operator Algebras," which appeared as Volume 100 - I and II in the series, Pure and Applied Mathematics, published by Academic Press in 1983 and 1986, respectively. As stated in the preface to those volumes, "Their primary goal is to teach the sub ject and lead the reader to the point where the vast recent research literature, both in the subject proper and in its many applications, becomes accessible." No attempt was made to be encyclopcedic; the choice of material was made from among the fundamentals of what may be called the "classical" theory of operator algebras. By way of supplementing the topics selected for presentation in "Fundamentals," a substantial list of exercises comprises the last section of each chapter. An equally important purpose of those exer cises is to develop "hand-on" skills in use ofthe techniques appearing in the text. As a consequence, each exercise was carefully designed to depend only on the material that precedes it, and separated into segments each of which is realistically capable of solution by an at tentive, diligent, well-motivated reader.

Author : Masamichi Takesaki
Publisher : Springer Science & Business Media
Page : 424 pages
File Size : 55,5 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.

Author : Richard V. Kadison,John R. Ringrose
Publisher : Unknown
Page : 398 pages
File Size : 50,8 Mb
Release : 1997
Category : Electronic
ISBN : 0821808192

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Elementary Theory by Richard V. Kadison,John R. Ringrose Pdf

Author : Serban Stratila
Publisher : Cambridge University Press
Page : 461 pages
File Size : 51,6 Mb
Release : 2020-12-03
Category : Mathematics
ISBN : 9781108489607

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Modular Theory in Operator Algebras by Serban Stratila Pdf

The first edition of this book appeared in 1981 as a direct continuation of Lectures of von Neumann Algebras (by Ş.V. Strătilă and L. Zsid ) and, until 2003, was the only comprehensive monograph on the subject. Addressing the students of mathematics and physics and researchers interested in operator algebras, noncommutative geometry and free probability, this revised edition covers the fundamentals and latest developments in the field of operator algebras. It discusses the group-measure space construction, Krieger factors, infinite tensor products of factors of type I (ITPFI factors) and construction of the type III_1 hyperfinite factor. It also studies the techniques necessary for continuous and discrete decomposition, duality theory for noncommutative groups, discrete decomposition of Connes, and Ocneanu's result on the actions of amenable groups. It contains a detailed consideration of groups of automorphisms and their spectral theory, and the theory of crossed products.

Author : Richard V. Kadison,John R. Ringrose
Publisher : American Mathematical Soc.
Page : 606 pages
File Size : 48,6 Mb
Release : 1998
Category : Mathematics
ISBN : 0821809911

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Fundamentals of the Theory of Operator Algebras by Richard V. Kadison,John R. Ringrose Pdf

This volume is the companion volume to Fundamentals of the Theory of Operator Algebras - Volume I: Elementary Theory. The goal of the text is to teach the subject and lead readers to where the literature - in the subject specifically and in its many applications - becomes accessible. The choice of material was made from among the fundamentals of what may be called the classical theory of operator algebras. This volume contains written solutions to the exercises in the Fundamentals of the Theory of Operator Algebras. Volume I: Elementary Theory.

Author : Gerald J. Murphy
Publisher : Academic Press
Page : 297 pages
File Size : 41,7 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 : Bingren Li
Publisher : World Scientific
Page : 264 pages
File Size : 54,7 Mb
Release : 2003
Category : Mathematics
ISBN : 9812795189

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Real Operator Algebras by Bingren Li Pdf

Since the treatment is from the beginning (real Banach and Hilbert spaces, real Banach algebras,

Author : Klaas Landsman
Publisher : Unknown
Page : 880 pages
File Size : 42,9 Mb
Release : 2020-10-09
Category : Science
ISBN : 1013278364

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Foundations of Quantum Theory by Klaas Landsman Pdf

This book studies the foundations of quantum theory through its relationship to classical physics. This idea goes back to the Copenhagen Interpretation (in the original version due to Bohr and Heisenberg), which the author relates to the mathematical formalism of operator algebras originally created by von Neumann. The book therefore includes comprehensive appendices on functional analysis and C*-algebras, as well as a briefer one on logic, category theory, and topos theory. Matters of foundational as well as mathematical interest that are covered in detail include symmetry (and its "spontaneous" breaking), the measurement problem, the Kochen-Specker, Free Will, and Bell Theorems, the Kadison-Singer conjecture, quantization, indistinguishable particles, the quantum theory of large systems, and quantum logic, the latter in connection with the topos approach to quantum theory. This work was published by Saint Philip Street Press pursuant to a Creative Commons license permitting commercial use. All rights not granted by the work's license are retained by the author or authors.

Author : Raymond C. Fabec
Publisher : CRC Press
Page : 309 pages
File Size : 47,9 Mb
Release : 2018-10-03
Category : Mathematics
ISBN : 9781351990219

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Fundamentals of Infinite Dimensional Representation Theory by Raymond C. Fabec Pdf

Infinite dimensional representation theory blossomed in the latter half of the twentieth century, developing in part with quantum mechanics and becoming one of the mainstays of modern mathematics. Fundamentals of Infinite Dimensional Representation Theory provides an accessible account of the topics in analytic group representation theory and operator algebras from which much of the subject has evolved. It presents new and old results in a coherent and natural manner and studies a number of tools useful in various areas of this diversely applied subject. From Borel spaces and selection theorems to Mackey's theory of induction, measures on homogeneous spaces, and the theory of left Hilbert algebras, the author's self-contained treatment allows readers to choose from a wide variety of topics and pursue them independently according to their needs. Beyond serving as both a general reference and as a text for those requiring a background in group-operator algebra representation theory, for careful readers, this monograph helps reveal not only the subject's utility, but also its inherent beauty.

Author : James Lepowsky,Haisheng Li
Publisher : Springer Science & Business Media
Page : 330 pages
File Size : 50,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9780817681869

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Introduction to Vertex Operator Algebras and Their Representations by James Lepowsky,Haisheng Li Pdf

* Introduces the fundamental theory of vertex operator algebras and its basic techniques and examples. * Begins with a detailed presentation of the theoretical foundations and proceeds to a range of applications. * Includes a number of new, original results and brings fresh perspective to important works of many other researchers in algebra, lie theory, representation theory, string theory, quantum field theory, and other areas of math and physics.

Author : Anonim
Publisher : Academic Press
Page : 691 pages
File Size : 48,5 Mb
Release : 1986-06-10
Category : Mathematics
ISBN : 9780080874173

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Fundamentals of the Theory of Operator Algebras. V2 by Anonim Pdf

Fundamentals of the Theory of Operator Algebras. V2

Author : Kehe Zhu
Publisher : CRC Press
Page : 172 pages
File Size : 53,5 Mb
Release : 1993-05-27
Category : Mathematics
ISBN : 0849378753

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An Introduction to Operator Algebras by Kehe Zhu Pdf

An Introduction to Operator Algebras is a concise text/reference that focuses on the fundamental results in operator algebras. Results discussed include Gelfand's representation of commutative C*-algebras, the GNS construction, the spectral theorem, polar decomposition, von Neumann's double commutant theorem, Kaplansky's density theorem, the (continuous, Borel, and L8) functional calculus for normal operators, and type decomposition for von Neumann algebras. Exercises are provided after each chapter.

Author : Richard V. Kadison,John R. Ringrose
Publisher : Elsevier
Page : 416 pages
File Size : 55,9 Mb
Release : 2016-06-03
Category : Mathematics
ISBN : 9781483214092

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Elementary Theory by Richard V. Kadison,John R. Ringrose Pdf

Fundamentals of the Theory of Operator Algebras, Volume I: Elementary Theory provides information pertinent to the fundamental aspects of the theory of operator algebras. This book discusses the finite-dimensional linear algebra. Organized into five chapters, this volume begins with an overview of the fundamental aspects of linear functional analysis that are needed in the study of operator algebras. This text then discusses the continuous linear operators, continuous linear functionals, weak topologies, and convexity in the context of linear topological spaces. Other chapters consider the elementary geometry of Hilbertspaces and the simplest properties of Hilbert space operators. This book discusses as well algebras that have a Banach-space structure relative to which the multiplication is continuous. The final chapter deals with those C*-algebras that are strong-operator closed in their action on some Hilbert space, which play a fundamental role in the subject. This book is a valuable resource for mathematicians.