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Author : Richard V. Kadison
Publisher : American Mathematical Soc.
Page : 798 pages
File Size : 41,7 Mb
Release : 1982
Category : Mathematics
ISBN : 0821814419
Author : Deguang Han,Palle E. T. Jørgensen,David R. Larson
Publisher : American Mathematical Soc.
Page : 440 pages
File Size : 42,7 Mb
Release : 2006
Category : Mathematics
ISBN : 9780821839232
This book offers a presentation of some new trends in operator theory and operator algebras, with a view to their applications. It consists of separate papers written by some of the leading practitioners in the field. The content is put together by the three editors in a way that should help students and working mathematicians in other parts of the mathematical sciences gain insight into an important part of modern mathematics and its applications. While different specialist authors are outlining new results in this book, the presentations have been made user friendly with the aid of tutorial material. In fact, each paper contains three things: a friendly introduction with motivation, tutorial material, and new research. The authors have strived to make their results relevant to the rest of mathematics. A list of topics discussed in the book includes wavelets, frames and their applications, quantum dynamics, multivariable operator theory, $C*$-algebras, and von Neumann algebras. Some longer papers present recent advances on particular, long-standing problems such as extensions and dilations, the Kadison-Singer conjecture, and diagonals of self-adjoint operators.
Author : Richard V. Kadison
Publisher : American Mathematical Soc.
Page : 808 pages
File Size : 44,9 Mb
Release : 1982
Category : Mathematics
ISBN : 0821814443
Author : David E. Evans,Masamichi Takesaki
Publisher : Cambridge University Press
Page : 257 pages
File Size : 48,5 Mb
Release : 1988
Category : Mathematics
ISBN : 9780521368438
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 : Aristides Katavolos
Publisher : Springer
Page : 490 pages
File Size : 50,5 Mb
Release : 1997-06-30
Category : Mathematics
ISBN : UOM:39015041312250
The proceedings of the August 1996 conference contain the 15 contributions of the main speakers. Themes include operator spaces; abstract operator algebras and their Hilbert modules; interaction with ring theory; non-self-adjoint operator algebras (limit algebras, reflexive algebras and subspaces, relations to basis theory); C*- algebraic quantum groups; endomorphisms of operator algebras, conditional expectations and projection maps; and applications, particularly to wavelet theory. A special lecture given by Stelios Negrepontis on the Pythagoreans is also presented. Annotation copyrighted by Book News, Inc., Portland, OR
Author : Masamichi Takesaki
Publisher : Springer Science & Business Media
Page : 424 pages
File Size : 42,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461261889
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 : Summer Research Institute on Operator Theory/Operator Algebras and Applications
Publisher : Unknown
Page : 654 pages
File Size : 54,8 Mb
Release : 2014-06-05
Category : MATHEMATICS
ISBN : 0821894293
Author : Peter A. Fillmore,James A. Mingo
Publisher : American Mathematical Soc.
Page : 335 pages
File Size : 55,8 Mb
Release : 1997
Category : Operator algebras
ISBN : 9780821805220
The study of operator algebras, which grew out of von Neumann's work in the 1920s and 30s on modelling quantum mechanics, has in recent years experienced tremendous growth and vitality, with significant applications in other areas both within mathematics and in other fields. For this reason, and because of the existence of a strong Canadian school in the subject, the topic was a natural candidate for an emphasis year at The Fields Institute. This volume is the second selection of papers that arose from the seminars and work-shops of a year-long program, Operator Algebras and Applications, that took place at The Fields Institute.
Author : Richard V. Kadison
Publisher : American Mathematical Soc.
Page : 654 pages
File Size : 53,5 Mb
Release : 1982
Category : Mathematics
ISBN : 9780821814413
Author : Erik M. Alfsen,Frederik W. Shultz
Publisher : Springer Science & Business Media
Page : 372 pages
File Size : 50,6 Mb
Release : 2001-04-27
Category : Mathematics
ISBN : 0817638903
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.
Author : Erik M. Alfsen,Frederic W. Shultz
Publisher : Springer Science & Business Media
Page : 467 pages
File Size : 54,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461200192
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.
Author : Maria Amélia Bastos,Israel Gohberg,Amarino Brites Lebre,Frank-Olme Speck
Publisher : Springer Science & Business Media
Page : 437 pages
File Size : 52,8 Mb
Release : 2008-05-27
Category : Mathematics
ISBN : 9783764386849
This book is composed of three survey lecture courses and some twenty invited research papers presented to WOAT 2006 - the International Summer School and Workshop on Operator Algebras, Operator Theory and Applications, held at Lisbon in September 2006. The volume reflects recent developments in the area of operator algebras and their interaction with research fields in complex analysis and operator theory. The book is aimed at postgraduates and researchers in these fields.
Author : M. Amélia Bastos,Amarino Lebre,Stefan Samko,Ilya M. Spitkovsky
Publisher : Springer
Page : 373 pages
File Size : 49,5 Mb
Release : 2014-05-23
Category : Mathematics
ISBN : 9783034808163
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 : Carlos André,M. Amélia Bastos,Alexei Yu. Karlovich,Bernd Silbermann,Ion Zaballa
Publisher : Birkhäuser
Page : 372 pages
File Size : 44,5 Mb
Release : 2018-08-22
Category : Mathematics
ISBN : 9783319724492
This book consists of invited survey articles and research papers in the scientific areas of the “International Workshop on Operator Algebras, Operator Theory and Applications,” which was held in Lisbon in July 2016. Reflecting recent developments in the field of algebras of operators, operator theory and matrix theory, it particularly focuses on groupoid algebras and Fredholm conditions, algebras of approximation sequences, C* algebras of convolution type operators, index theorems, spectrum and numerical range of operators, extreme supercharacters of infinite groups, quantum dynamics and operator algebras, and inverse eigenvalue problems. Establishing bridges between the three related areas of operator algebras, operator theory, and matrix theory, the book is aimed at researchers and graduate students who use results from these areas.
Author : James Lepowsky,Haisheng Li
Publisher : Springer Science & Business Media
Page : 330 pages
File Size : 45,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9780817681869
* 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.