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Author : Donald Bures
Publisher : American Mathematical Soc.
ISBN 13 : 0821818104
Total Pages : 127 pages
Book Rating : 4.8/5 (218 download)
Download or read book Abelian Subalgebras of Von Neumann Algebras written by Donald Bures and published by American Mathematical Soc.. This book was released on 1971 with total page 127 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Allan Sinclair
Publisher : Cambridge University Press
ISBN 13 : 0521719194
Total Pages : 411 pages
Book Rating : 4.5/5 (217 download)
Download or read book Finite Von Neumann Algebras and Masas written by Allan Sinclair and published by Cambridge University Press. This book was released on 2008-06-26 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first book devoted to the general theory of finite von Neumann algebras.
Author : M. Rordam
Publisher : Springer Science & Business Media
ISBN 13 : 3662048256
Total Pages : 206 pages
Book Rating : 4.6/5 (62 download)
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.
Author : Igor Fulman
Publisher : American Mathematical Soc.
ISBN 13 : 0821805576
Total Pages : 107 pages
Book Rating : 4.8/5 (218 download)
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.
Author : Șerban Strătilă
Publisher : Cambridge University Press
ISBN 13 : 1108496849
Total Pages : 441 pages
Book Rating : 4.1/5 (84 download)
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.
Author : Hans Halvorson
Publisher : Cambridge University Press
ISBN 13 : 113949922X
Total Pages : 487 pages
Book Rating : 4.1/5 (394 download)
Download or read book Deep Beauty written by Hans Halvorson and published by Cambridge University Press. This book was released on 2011-04-18 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: No scientific theory has caused more puzzlement and confusion than quantum theory. Physics is supposed to help us to understand the world, but quantum theory makes it seem a very strange place. This book is about how mathematical innovation can help us gain deeper insight into the structure of the physical world. Chapters by top researchers in the mathematical foundations of physics explore new ideas, especially novel mathematical concepts at the cutting edge of future physics. These creative developments in mathematics may catalyze the advances that enable us to understand our current physical theories, especially quantum theory. The authors bring diverse perspectives, unified only by the attempt to introduce fresh concepts that will open up new vistas in our understanding of future physics.
Author : J. Dixmier
Publisher : Elsevier
ISBN 13 : 0080960154
Total Pages : 479 pages
Book Rating : 4.0/5 (89 download)
Download or read book Von Neumann Algebras written by J. Dixmier and published by Elsevier. This book was released on 2011-08-18 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, we study, under the name of von Neumann algebras, those algebras generally known as “rings of operators“ or “W*-algebras.“ The new terminology, suggested by J. Dieudonng, is fully justified from the historical point of view. Certain of the results are valid for more general algebras. We have, however systematically avoided this kind of generalization, except when it would facilitate the study of von Neumann algebras themselves. Parts I and I1 comprise those results which at present appear to’be the most useful for applications, although we do not embark on the study of those applications. Part 111, which is more technical, is primarily intended for specialists; it is virtually independent of Part 11.
Author : Bruce Blackadar
Publisher : Taylor & Francis
ISBN 13 : 9783540284864
Total Pages : 552 pages
Book Rating : 4.2/5 (848 download)
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.
Author : Adrian Ocneanu
Publisher : Springer
ISBN 13 : 3540395792
Total Pages : 120 pages
Book Rating : 4.5/5 (43 download)
Download or read book Actions of Discrete Amenable Groups on von Neumann Algebras written by Adrian Ocneanu and published by Springer. This book was released on 2006-12-08 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Richard V. Kadison
Publisher : American Mathematical Soc.
ISBN 13 : 1470420732
Total Pages : 700 pages
Book Rating : 4.4/5 (74 download)
Download or read book Fundamentals of the Theory of Operator Algebras Vollume II written by Richard V. Kadison and published by American Mathematical Soc.. This book was released on 2015-03-28 with total page 700 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second part of this two-volume work presents an introduction to functional analysis and the initial fundamentals of C ]* - and Von Neumann algebra theory in a form suitable for both intermediate graduate courses and self-study. The authors provide a clear account of the introductory portions of this important and technically difficult subject. Well supplied with exercises, the text assumes only basic measure theory and topology. The books present the possibility for the design of numerous courses aimed at different audiences.
Author : Huaxin Lin
Publisher : World Scientific
ISBN 13 : 9789812799883
Total Pages : 336 pages
Book Rating : 4.7/5 (998 download)
Download or read book An Introduction to the Classification of Amenable C*-algebras written by Huaxin Lin and published by World Scientific. This book was released on 2001 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory and applications of C Oeu -algebras are related to fields ranging from operator theory, group representations and quantum mechanics, to non-commutative geometry and dynamical systems. By Gelfand transformation, the theory of C Oeu -algebras is also regarded as non-commutative topology. About a decade ago, George A. Elliott initiated the program of classification of C Oeu -algebras (up to isomorphism) by their K -theoretical data. It started with the classification of AT -algebras with real rank zero. Since then great efforts have been made to classify amenable C Oeu -algebras, a class of C Oeu -algebras that arises most naturally. For example, a large class of simple amenable C Oeu -algebras is discovered to be classifiable. The application of these results to dynamical systems has been established. This book introduces the recent development of the theory of the classification of amenable C Oeu -algebras OCo the first such attempt. The first three chapters present the basics of the theory of C Oeu -algebras which are particularly important to the theory of the classification of amenable C Oeu -algebras. Chapter 4 otters the classification of the so-called AT -algebras of real rank zero. The first four chapters are self-contained, and can serve as a text for a graduate course on C Oeu -algebras. The last two chapters contain more advanced material. In particular, they deal with the classification theorem for simple AH -algebras with real rank zero, the work of Elliott and Gong. The book contains many new proofs and some original results related to the classification of amenable C Oeu -algebras. Besides being as an introduction to the theory of the classification of amenable C Oeu -algebras, it is a comprehensive reference for those more familiar with the subject. Sample Chapter(s). Chapter 1.1: Banach algebras (260 KB). Chapter 1.2: C*-algebras (210 KB). Chapter 1.3: Commutative C*-algebras (212 KB). Chapter 1.4: Positive cones (207 KB). Chapter 1.5: Approximate identities, hereditary C*-subalgebras and quotients (230 KB). Chapter 1.6: Positive linear functionals and a Gelfand-Naimark theorem (235 KB). Chapter 1.7: Von Neumann algebras (234 KB). Chapter 1.8: Enveloping von Neumann algebras and the spectral theorem (217 KB). Chapter 1.9: Examples of C*-algebras (270 KB). Chapter 1.10: Inductive limits of C*-algebras (252 KB). Chapter 1.11: Exercises (220 KB). Chapter 1.12: Addenda (168 KB). Contents: The Basics of C Oeu -Algebras; Amenable C Oeu -Algebras and K -Theory; AF- Algebras and Ranks of C Oeu -Algebras; Classification of Simple AT -Algebras; C Oeu -Algebra Extensions; Classification of Simple Amenable C Oeu -Algebras. Readership: Researchers and graduate students in operator algebras."
Author : Masamichi Takesaki
Publisher : Springer Science & Business Media
ISBN 13 : 9783540429142
Total Pages : 552 pages
Book Rating : 4.4/5 (291 download)
Download or read book Theory of Operator Algebras II written by Masamichi Takesaki and published by Springer Science & Business Media. This book was released on 2002-11-01 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: Together with Theory of Operator Algebras I and III, this book presents the theory of von Neumann algebras and non-commutative integration focusing on the group of automorphisms and the structure analysis. From the reviews: "These books can be warmly recommended to every graduate student who wants to become acquainted with this exciting branch of mathematics. Furthermore, they should be on the bookshelf of every researcher of the area." --ACTA SCIENTIARUM MATHEMATICARUM
Author : Marco Stevens
Publisher : Springer
ISBN 13 : 3319477021
Total Pages : 140 pages
Book Rating : 4.3/5 (194 download)
Download or read book The Kadison-Singer Property written by Marco Stevens and published by Springer. This book was released on 2016-11-07 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a complete classification of all algebras with the Kadison-Singer property, when restricting to separable Hilbert spaces. The Kadison-Singer property deals with the following question: given a Hilbert space H and an abelian unital C*-subalgebra A of B(H), does every pure state on A extend uniquely to a pure state on B(H)? This question has deep connections to fundamental aspects of quantum physics, as is explained in the foreword by Klaas Landsman. The book starts with an accessible introduction to the concept of states and continues with a detailed proof of the classification of maximal Abelian von Neumann algebras, a very explicit construction of the Stone-Cech compactification and an account of the recent proof of the Kadison-Singer problem. At the end accessible appendices provide the necessary background material. This elementary account of the Kadison-Singer conjecture is very well-suited for graduate students interested in operator algebras and states, researchers who are non-specialists of the field, and/or interested in fundamental quantum physics.
Author : Gerald J. Murphy
Publisher : Academic Press
ISBN 13 : 0080924964
Total Pages : 297 pages
Book Rating : 4.0/5 (89 download)
Download or read book C*-Algebras and Operator Theory written by Gerald J. Murphy and published by Academic Press. This book was released on 2014-06-28 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Alain Connes
Publisher : Springer Science & Business Media
ISBN 13 : 9783540203575
Total Pages : 372 pages
Book Rating : 4.2/5 (35 download)
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.
Author : G.G. Emch
Publisher : Elsevier
ISBN 13 : 0080872115
Total Pages : 561 pages
Book Rating : 4.0/5 (88 download)
Download or read book Mathematical and Conceptual Foundations of 20th-Century Physics written by G.G. Emch and published by Elsevier. This book was released on 2000-04-01 with total page 561 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is primarily intended for Mathematicians, but students in the physical sciences will find here information not usually available in physics texts.The main aim of this book is to provide a unified mathematical account of the conceptual foundations of 20th-Century Physics, in a form suitable for a one-year survey course in Mathematics or Mathematical Physics. Emphasis is laid on the interlocked historical development of mathematical and physical ideas.
Author : William Arveson
Publisher : American Mathematical Soc.
ISBN 13 : 9780821889008
Total Pages : 108 pages
Book Rating : 4.8/5 (89 download)
Download or read book Ten Lectures on Operator Algebras written by William Arveson and published by American Mathematical Soc.. This book was released on 1984 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains expanded versions of ten lectures delivered at Texas Tech University in the summer of 1983. The operator algebras of the title are nonselfadjoint algebras of operators on Hilbert space.
