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Continuous Crossed Products And Type Iii Von Neumann Algebras
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Book Synopsis Continuous Crossed Products and Type III Von Neumann Algebras by : Alfons van Daele
Download or read book Continuous Crossed Products and Type III Von Neumann Algebras written by Alfons van Daele and published by Cambridge University Press. This book was released on 1978-07-20 with total page 81 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes, based on lectures given at the University of Newcastle upon Tyne, provide an introduction to the theory of von Neumann algebras.
Book Synopsis Continuous Crossed Products and Type III Von Neumann Algebras by : Alfons van Daele
Download or read book Continuous Crossed Products and Type III Von Neumann Algebras written by Alfons van Daele and published by . This book was released on 2014-05-14 with total page 77 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes, based on lectures given at the University of Newcastle upon Tyne, provide an introduction to the theory of von Neumann algebras.
Book Synopsis Lectures on von Neumann Algebras by : Șerban Strătilă
Download or read book Lectures on von Neumann Algebras written by Șerban Strătilă and published by Cambridge University Press. This book was released on 2019-05-09 with total page 441 pages. Available in PDF, EPUB and Kindle. Book excerpt: The text covers fundamentals of von Neumann algebras, including the Tomita's theory of von Neumann algebras and the latest developments.
Book Synopsis Crossed Products of von Neumann Algebras by Equivalence Relations and Their Subalgebras by : Igor Fulman
Download or read book Crossed Products of von Neumann Algebras by Equivalence Relations and Their Subalgebras written by Igor Fulman and published by American Mathematical Soc.. This book was released on 1997 with total page 107 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, the author introduces and studies the construction of the crossed product of a von Neumann algebra $M = \int _X M(x)d\mu (x)$ by an equivalence relation on $X$ with countable cosets. This construction is the generalization of the construction of the crossed product of an abelian von Neumann algebra by an equivalence relation introduced by J. Feldman and C. C. Moore. Many properties of this construction are proved in the general case. In addition, the generalizations of the Spectral Theorem on Bimodules and of the theorem on dilations are proved.
Book Synopsis Fundamentals of the Theory of Operator Algebras. V2 by :
Download or read book Fundamentals of the Theory of Operator Algebras. V2 written by and published by Academic Press. This book was released on 1986-06-10 with total page 691 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fundamentals of the Theory of Operator Algebras. V2
Book Synopsis An Invitation to von Neumann Algebras by : V.S. Sunder
Download or read book An Invitation to von Neumann Algebras written by V.S. Sunder and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Operator Algebras by : Bruce Blackadar
Download or read book Operator Algebras written by Bruce Blackadar and published by Taylor & Francis. This book was released on 2006 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Classification of Nuclear C*-Algebras. Entropy in Operator Algebras by : M. Rordam
Download or read book Classification of Nuclear C*-Algebras. Entropy in Operator Algebras written by M. Rordam and published by Springer Science & Business Media. This book was released on 2013-04-18 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Fundamentals of the Theory of Operator Algebras. Volume II by : Richard V. Kadison
Download or read book Fundamentals of the Theory of Operator Algebras. Volume II written by Richard V. Kadison and published by American Mathematical Soc.. This book was released on 1997 with total page 702 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume two of the two-volume set (see ISBN 0-8218-0819-2) covers the comparison theory of projection, normal states and unitary equivalence of von Newmann algebras, the trade, algebra and commutant, special representation of C*-algebras, tensor products, approximation by matrix algebras, crossed products, and direct integrals and decompositions. Originally published by Academic Press in 1986. Annotation copyrighted by Book News, Inc., Portland, OR
Book Synopsis Crossed Products of C*-algebras by : Dana P. Williams
Download or read book Crossed Products of C*-algebras written by Dana P. Williams and published by American Mathematical Soc.. This book was released on 2007 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Theory of Operator Algebras I by : Masamichi Takesaki
Download or read book Theory of Operator Algebras I written by Masamichi Takesaki and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Noncommutative Geometry by : Alain Connes
Download or read book Noncommutative Geometry written by Alain Connes and published by Springer Science & Business Media. This book was released on 2003-12-08 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Fundamentals of the Theory of Operator Algebras by : KADISON
Download or read book Fundamentals of the Theory of Operator Algebras written by KADISON and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 599 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Lectures on von Neumann Algebras by : Serban-Valentin Stratila
Download or read book Lectures on von Neumann Algebras written by Serban-Valentin Stratila and published by Cambridge University Press. This book was released on 2019-05-09 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written in lucid language, this valuable text discusses fundamental concepts of von Neumann algebras including bounded linear operators in Hilbert spaces, finite von Neumann algebras, linear forms on algebra of operators, geometry of projections and classification of von Neumann algebras in an easy to understand manner. The revised text covers new material including the first two examples of factors of type II^1, an example of factor of type III and theorems for von Neumann algebras with a cyclic and separating vector. Pedagogical features including solved problems and exercises are interspersed throughout the book.
Book Synopsis Duality for Crossed Products of Von Neumann Algebras by : Y. Nakagami
Download or read book Duality for Crossed Products of Von Neumann Algebras written by Y. Nakagami and published by . This book was released on 2014-01-15 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Fundamentals of the Theory of Operator Algebras. Volume IV by : Richard V. Kadison
Download or read book Fundamentals of the Theory of Operator Algebras. Volume IV written by Richard V. Kadison and published by American Mathematical Soc.. This book was released on 1998-01-13 with total page 604 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Algebra and Operator Theory by : Y. Khakimdjanov
Download or read book Algebra and Operator Theory written by Y. Khakimdjanov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the lectures given during the second French-Uzbek Colloquium on Algebra and Operator Theory which took place in Tashkent in 1997, at the Mathematical Institute of the Uzbekistan Academy of Sciences. Among the algebraic topics discussed here are deformation of Lie algebras, cohomology theory, the algebraic variety of the laws of Lie algebras, Euler equations on Lie algebras, Leibniz algebras, and real K-theory. Some contributions have a geometrical aspect, such as supermanifolds. The papers on operator theory deal with the study of certain types of operator algebras. This volume also contains a detailed introduction to the theory of quantum groups. Audience: This book is intended for graduate students specialising in algebra, differential geometry, operator theory, and theoretical physics, and for researchers in mathematics and theoretical physics.