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Author: Alfons van Daele Publisher: Cambridge University Press ISBN: 0521219752 Category : Mathematics Languages : en Pages : 81
Book Description
These notes, based on lectures given at the University of Newcastle upon Tyne, provide an introduction to the theory of von Neumann algebras.
Author: Alfons van Daele Publisher: Cambridge University Press ISBN: 0521219752 Category : Mathematics Languages : en Pages : 81
Book Description
These notes, based on lectures given at the University of Newcastle upon Tyne, provide an introduction to the theory of von Neumann algebras.
Author: Alfons van Daele Publisher: ISBN: 9781107360891 Category : MATHEMATICS Languages : en Pages : 77
Book Description
These notes, based on lectures given at the University of Newcastle upon Tyne, provide an introduction to the theory of von Neumann algebras.
Author: V.S. Sunder Publisher: Springer Science & Business Media ISBN: 1461386691 Category : Mathematics Languages : en Pages : 184
Book Description
Why This Book: The theory of von Neumann algebras has been growing in leaps and bounds in the last 20 years. It has always had strong connections with ergodic theory and mathematical physics. It is now beginning to make contact with other areas such as differential geometry and K-Theory. There seems to be a strong case for putting together a book which (a) introduces a reader to some of the basic theory needed to appreciate the recent advances, without getting bogged down by too much technical detail; (b) makes minimal assumptions on the reader's background; and (c) is small enough in size to not test the stamina and patience of the reader. This book tries to meet these requirements. In any case, it is just what its title proclaims it to be -- an invitation to the exciting world of von Neumann algebras. It is hoped that after perusing this book, the reader might be tempted to fill in the numerous (and technically, capacious) gaps in this exposition, and to delve further into the depths of the theory. For the expert, it suffices to mention here that after some preliminaries, the book commences with the Murray - von Neumann classification of factors, proceeds through the basic modular theory to the III). classification of Connes, and concludes with a discussion of crossed-products, Krieger's ratio set, examples of factors, and Takesaki's duality theorem.
Author: Bruce Blackadar Publisher: Taylor & Francis ISBN: 9783540284864 Category : Mathematics Languages : en Pages : 552
Book Description
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: M. Rordam Publisher: Springer Science & Business Media ISBN: 3662048256 Category : Mathematics Languages : en Pages : 206
Book Description
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: Source Wikipedia Publisher: University-Press.org ISBN: 9781230512310 Category : Languages : en Pages : 28
Book Description
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 26. Chapters: Abelian von Neumann algebra, Affiliated operator, Baer ring, Central carrier, Commutation theorem, Connes embedding problem, Continuous geometry, Crossed product, Direct integral, Dixmier trace, Finite dimensional von Neumann algebra, Hyperfinite type II factor, Kaplansky density theorem, Octacube (mathematics), Schroder-Bernstein theorems for operator algebras, Sherman-Takeda theorem, Subfactor, Temperley-Lieb algebra, Tomita-Takesaki theory, Ultrastrong topology, Ultraweak topology, Von Neumann bicommutant theorem.
Author: Dana P. Williams Publisher: American Mathematical Soc. ISBN: 0821842420 Category : Mathematics Languages : en Pages : 546
Book Description
The theory of crossed products is extremely rich and intriguing. There are applications not only to operator algebras, but to subjects as varied as noncommutative geometry and mathematical physics. This book provides a detailed introduction to this vast subject suitable for graduate students and others whose research has contact with crossed product $C*$-algebras. in addition to providing the basic definitions and results, the main focus of this book is the fine ideal structure of crossed products as revealed by the study of induced representations via the Green-Mackey-Rieffel machine. in particular, there is an in-depth analysis of the imprimitivity theorems on which Rieffel's theory of induced representations and Morita equivalence of $C*$-algebras are based. There is also a detailed treatment of the generalized Effros-Hahn conjecture and its proof due to Gootman, Rosenberg, and Sauvageot. This book is meant to be self-contained and accessible to any graduate student coming out of a first course on operator algebras. There are appendices that deal with ancillary subjects, which while not central to the subject, are nevertheless crucial for a complete understanding of the material. Some of the appendices will be of independent interest. to view another book by this author, please visit Morita Equivalence and Continuous-Trace $C*$-Algebras.
Author: Masamichi Takesaki Publisher: Springer Science & Business Media ISBN: 1461261880 Category : Mathematics Languages : en Pages : 424
Book Description
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: Alfons van Daele
Author: Alfons van Daele
Author: Alfons van Daele
Author: V.S. Sunder
Author: Serban Stratila
Author: Bruce Blackadar
Author: M. Rordam
Author: Igor Fulman
Author: Source Wikipedia
Author: Dana P. Williams
Author: Masamichi Takesaki