Operator Algebras And Mathematical Physics

Author : Tirthankar Bhattacharyya,Michael A. Dritschel
Publisher : Birkhäuser
Page : 202 pages
File Size : 53,6 Mb
Release : 2015-09-29
Category : Mathematics
ISBN : 9783319181820

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Operator Algebras and Mathematical Physics by Tirthankar Bhattacharyya,Michael A. Dritschel Pdf

This volume gathers contributions from the International Workshop on Operator Theory and Its Applications (IWOTA) held in Bangalore, India, in December 2013. All articles were written by experts and cover a broad range of original material at the cutting edge of operator theory and its applications. Topics include multivariable operator theory, operator theory on indefinite metric spaces (Krein and Pontryagin spaces) and its applications, spectral theory with applications to differential operators, the geometry of Banach spaces, scattering and time varying linear systems, and wavelets and coherent states.

Author : Palle E. T. Jørgensen,Paul S. Muhly
Publisher : Unknown
Page : 564 pages
File Size : 52,8 Mb
Release : 1987
Category : Banach algebras
ISBN : UCAL:B5008524

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Operator Algebras and Mathematical Physics by Palle E. T. Jørgensen,Paul S. Muhly Pdf

This volume contains papers presented at the University of Iowa 1985 Summer Conference in honor of H.-J. Borchers, N. M. Hugenholtz, R. V. Kadison, and D. Kastler and gives a systematic, up-to-date treatment of the fruitful interaction that the last two decades have brought between operator algebras and mathematical physics. Special attention is paid to an overview of the algebraic approach to quantum field theory and in particular, to quantum statistical mechanics. More than half the papers culminate with a presentation of new results which have not appeared previously in journals, and with a few exceptions, these new results are presented with complete proofs. This book is addressed to graduate students and researchers working in a broad spectrum of areas in mathematics and mathematical physics. Functional analysis, operator algebras, operator theory, differential geometry, cyclic cohomology, $K$-theory, and index theory are applied to questions in the quantum theory of fields and statistical mechanics. The individual papers are self-contained, but the reader should have some familiarity with the basic concepts of functional analysis and operator theory, although no physics background is assumed.

Author : Richard Herman,Betül Tanbay
Publisher : CRC Press
Page : 336 pages
File Size : 53,7 Mb
Release : 1993-11-15
Category : Mathematics
ISBN : 9781439863510

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Operator Algebras, Mathematical Physics, and Low Dimensional Topology by Richard Herman,Betül Tanbay Pdf

This volume records the proceedings of an international conference that explored recent developments and the interaction between mathematical theory and physical phenomena.

Author : Ola Bratteli,Derek William Robinson
Publisher : Springer Science & Business Media
Page : 503 pages
File Size : 43,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783662023136

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Operator Algebras and Quantum Statistical Mechanics by Ola Bratteli,Derek William Robinson Pdf

In this book we describe the elementary theory of operator algebras and parts of the advanced theory which are of relevance, or potentially of relevance, to mathematical physics. Subsequently we describe various applications to quantum statistical mechanics. At the outset of this project we intended to cover this material in one volume but in the course of develop ment it was realized that this would entail the omission of various interesting topics or details. Consequently the book was split into two volumes, the first devoted to the general theory of operator algebras and the second to the applications. This splitting into theory and applications is conventional but somewhat arbitrary. In the last 15-20 years mathematical physicists have realized the importance of operator algebras and their states and automorphisms for problems offield theory and statistical mechanics. But the theory of 20 years ago was largely developed for the analysis of group representations and it was inadequate for many physical applications. Thus after a short honey moon period in which the new found tools of the extant theory were applied to the most amenable problems a longer and more interesting period ensued in which mathematical physicists were forced to redevelop the theory in relevant directions. New concepts were introduced, e. g. asymptotic abelian ness and KMS states, new techniques applied, e. g. the Choquet theory of barycentric decomposition for states, and new structural results obtained, e. g. the existence of a continuum of nonisomorphic type-three factors.

Author : Ola Bratteli,Derek William Robinson
Publisher : Springer Science & Business Media
Page : 510 pages
File Size : 49,8 Mb
Release : 2013-03-14
Category : Technology & Engineering
ISBN : 9783662025208

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Operator Algebras and Quantum Statistical Mechanics 1 by Ola Bratteli,Derek William Robinson Pdf

In this book we describe the elementary theory of operator algebras and parts of the advanced theory which are of relevance, or potentially of relevance, to mathematical physics. Subsequently we describe various applications to quantum statistical mechanics. At the outset of this project we intended to cover this material in one volume but in the course of develop ment it was realized that this would entail the omission ofvarious interesting topics or details. Consequently the book was split into two volumes, the first devoted to the general theory of operator algebras and the second to the applications. This splitting into theory and applications is conventional but somewhat arbitrary. In the last 15-20 years mathematical physicists have realized the importance of operator algebras and their states and automorphisms for problems of field theory and statistical mechanics. But the theory of 20 years aga was largely developed for the analysis of group representations and it was inadequate for many physical applications. Thus after a short honey moon period in which the new found tools of the extant theory were applied to the most amenable problems a longer and more interesting period ensued in which mathematical physicists were forced to redevelop the theory in relevant directions. New concepts were introduced, e. g. asymptotic abelian ness and KMS states, new techniques applied, e. g. the Choquet theory of barycentric decomposition for states, and new structural results obtained, e. g. the existence of a continuum of nonisomorphic type-three factors.

Author : Ola Bratteli,Derek William Robinson
Publisher : Springer Science & Business Media
Page : 536 pages
File Size : 45,7 Mb
Release : 2003-01-09
Category : Science
ISBN : 3540614435

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Operator Algebras and Quantum Statistical Mechanics by Ola Bratteli,Derek William Robinson Pdf

For almost two decades, this has been the classical textbook on applications of operator algebra theory to quantum statistical physics. Major changes in the new edition relate to Bose-Einstein condensation, the dynamics of the X-Y model and questions on phase transitions.

Author : Ola Bratteli,Derek William Robinson
Publisher : Springer Science & Business Media
Page : 525 pages
File Size : 54,8 Mb
Release : 2013-06-29
Category : Science
ISBN : 9783662034446

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Operator Algebras and Quantum Statistical Mechanics by Ola Bratteli,Derek William Robinson Pdf

For almost two decades, this has been the classical textbook on applications of operator algebra theory to quantum statistical physics. Major changes in the new edition relate to Bose-Einstein condensation, the dynamics of the X-Y model and questions on phase transitions.

Author : Masamichi Takesaki
Publisher : Springer Science & Business Media
Page : 424 pages
File Size : 43,6 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.

Author : M. Amélia Bastos,Amarino Lebre,Stefan Samko,Ilya M. Spitkovsky
Publisher : Springer
Page : 373 pages
File Size : 45,5 Mb
Release : 2014-05-23
Category : Mathematics
ISBN : 9783034808163

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Operator Theory, Operator Algebras and Applications by M. Amélia Bastos,Amarino Lebre,Stefan Samko,Ilya M. Spitkovsky Pdf

This book consists of research papers that cover the scientific areas of the International Workshop on Operator Theory, Operator Algebras and Applications, held in Lisbon in September 2012. The volume particularly focuses on (i) operator theory and harmonic analysis (singular integral operators with shifts; pseudodifferential operators, factorization of almost periodic matrix functions; inequalities; Cauchy type integrals; maximal and singular operators on generalized Orlicz-Morrey spaces; the Riesz potential operator; modification of Hadamard fractional integro-differentiation), (ii) operator algebras (invertibility in groupoid C*-algebras; inner endomorphisms of some semi group, crossed products; C*-algebras generated by mappings which have finite orbits; Folner sequences in operator algebras; arithmetic aspect of C*_r SL(2); C*-algebras of singular integral operators; algebras of operator sequences) and (iii) mathematical physics (operator approach to diffraction from polygonal-conical screens; Poisson geometry of difference Lax operators).

Author : Hitoshi Moriyoshi,Toshikazu Natsume
Publisher : American Mathematical Soc.
Page : 155 pages
File Size : 55,7 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.

Author : Masaki Izumi,Yasuyuki Kawahigashi,Motoko Kotani,Hiroki Matui,Narutaka Ozawa
Publisher : Unknown
Page : 128 pages
File Size : 55,6 Mb
Release : 2019
Category : Mathematical physics
ISBN : 4864970807

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Operator Algebras and Mathematical Physics by Masaki Izumi,Yasuyuki Kawahigashi,Motoko Kotani,Hiroki Matui,Narutaka Ozawa Pdf

Author : Calvin C. Moore
Publisher : Springer Science & Business Media
Page : 283 pages
File Size : 51,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461247227

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Group Representations, Ergodic Theory, Operator Algebras, and Mathematical Physics by Calvin C. Moore Pdf

The Mathematical Sciences Research Institute sponsored a three day conference, May 21-23, 1984 to honor Professor George W. Mackey. The title of the conference, Group Representations, Ergodic Theory, Operator Algebras, and Mathematical Physics, reflects the interests in science that have characterized Professor wide ranging Mackey's work. The conference provided an opportunity for his students, friends and colleagues to honor him and his contributions. The conference was attended by over one hundred people and the participants included five mathematical generations Professor Mackey's mathematical father, Marshall Stone, many mathematical children, grandchildren, and at least one mathematical great-grandchild. This volume is a compendium of the scientific papers presented at the conference plus some additional papers contributed after the conference. The far ranging scope of the various articles is a further indication of the large number of fields that have been affected by Professor Mackey's work. Calvin C. Moore Berkeley, CA Feb, 1986 Table of Contents Preface vi i Ambiguity Functions and Group L. Auslander and Representations R. Tolimieri Kirillov Orbits and Direct Integral Lawrence Corwin 11 Decompositions on Certain Quotient Spaces Some Homotopy and Shape Calculations Edward G. Effors and 69 for C*-Algebras Jerome Kaminker 121 Small Unitary Representations of Roger Howe Classical Groups Dual Vector Spaces Irving Kaplansky 151 Exponential Decay of Correlation Calvin C. Moore 163 Coefficients for Geodesic Flows Lattices in U(n. I) G. D. Mostow Induced Bundles and Nonlinear Irving E. Segal 199 Wave equations Compact Ahelian Aut.

Author : Yi-Zhi Huang,Kailash C. Misra
Publisher : American Mathematical Soc.
Page : 500 pages
File Size : 53,9 Mb
Release : 2007
Category : Lie algebras
ISBN : 9780821839867

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Lie Algebras, Vertex Operator Algebras and Their Applications by Yi-Zhi Huang,Kailash C. Misra Pdf

The articles in this book are based on talks given at the international conference 'Lie algebras, vertex operator algebras and their applications'. The focus of the papers is mainly on Lie algebras, quantum groups, vertex operator algebras and their applications to number theory, combinatorics and conformal field theory.

Author : Ola Bratteli,Derek William Robinson
Publisher : Springer Science & Business Media
Page : 508 pages
File Size : 45,8 Mb
Release : 2013-04-17
Category : Science
ISBN : 9783662090893

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Operator Algebras and Quantum Statistical Mechanics II by Ola Bratteli,Derek William Robinson Pdf

For almost two decades, this has been the classical textbook on applications of operator algebra theory to quantum statistical physics. Major changes in the new edition relate to Bose-Einstein condensation, the dynamics of the X-Y model and questions on phase transitions.

Author : Daniel Alpay,Fabio Cipriani,Fabrizio Colombo,Daniele Guido,Irene Sabadini,Jean-Luc Sauvageot
Publisher : Birkhäuser
Page : 283 pages
File Size : 53,7 Mb
Release : 2016-06-30
Category : Mathematics
ISBN : 9783319291161

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Noncommutative Analysis, Operator Theory and Applications by Daniel Alpay,Fabio Cipriani,Fabrizio Colombo,Daniele Guido,Irene Sabadini,Jean-Luc Sauvageot Pdf

This book illustrates several aspects of the current research activity in operator theory, operator algebras and applications in various areas of mathematics and mathematical physics. It is addressed to specialists but also to graduate students in several fields including global analysis, Schur analysis, complex analysis, C*-algebras, noncommutative geometry, operator algebras, operator theory and their applications. Contributors: F. Arici, S. Bernstein, V. Bolotnikov, J. Bourgain, P. Cerejeiras, F. Cipriani, F. Colombo, F. D'Andrea, G. Dell'Antonio, M. Elin, U. Franz, D. Guido, T. Isola, A. Kula, L.E. Labuschagne, G. Landi, W.A. Majewski, I. Sabadini, J.-L. Sauvageot, D. Shoikhet, A. Skalski, H. de Snoo, D. C. Struppa, N. Vieira, D.V. Voiculescu, and H. Woracek.