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Author: Daniel Redelmeier Publisher: ISBN: Category : Languages : en Pages :
Book Description
We examine the amalgamated free product of hyperfinite von Neumann algebras. First we describe the amalgamated free product of hyperfinite von Neumann algebras over finite dimensional subalgebras. In this case the result is always the direct sum of a hyperfinite von Neumann algebra and a finite number of interpolated free group factors. We then show that this class is closed under this type of amalgamated free product. After that we allow amalgamation over possibly infinite dimensional multimatrix subalgebras. In this case the product of two hyperfinite von Neumann algebras is the direct sum of a hyperfinite von Neumann algebra and a countable direct sum of interpolated free group factors. As before, we show that this class is closed under amalgamated free products over multimatrix algebras.
Author: Daniel Redelmeier Publisher: ISBN: Category : Languages : en Pages :
Book Description
We examine the amalgamated free product of hyperfinite von Neumann algebras. First we describe the amalgamated free product of hyperfinite von Neumann algebras over finite dimensional subalgebras. In this case the result is always the direct sum of a hyperfinite von Neumann algebra and a finite number of interpolated free group factors. We then show that this class is closed under this type of amalgamated free product. After that we allow amalgamation over possibly infinite dimensional multimatrix subalgebras. In this case the product of two hyperfinite von Neumann algebras is the direct sum of a hyperfinite von Neumann algebra and a countable direct sum of interpolated free group factors. As before, we show that this class is closed under amalgamated free products over multimatrix algebras.
Author: Dan V. Voiculescu Publisher: American Mathematical Soc. ISBN: 0821806750 Category : Mathematics Languages : en Pages : 322
Book Description
This is a volume of papers from a workshop on Random Matrices and Operator Algebra Free Products, held at The Fields Institute for Research in the Mathematical Sciences in March 1995. Over the last few years, there has been much progress on the operator algebra and noncommutative probability sides of the subject. New links with the physics of masterfields and the combinatorics of noncrossing partitions have emerged. Moreover there is a growing free entropy theory.
Author: 野水克己 Publisher: American Mathematical Soc. ISBN: 9780821827802 Category : Mathematical analysis Languages : en Pages : 148
Book Description
This volume contains papers that originally appeared in Japanese in the journal Sugaku. Ordinarily the papers would appear in the AMS translation of that journal, but to expedite publication, the Society has chosen to publish them as a volume of selected papers. The papers here are in the general area of mathematical analysis as it pertains to free probability theory.
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: Bruce Blackadar Publisher: Springer Science & Business Media ISBN: 3540285172 Category : Mathematics Languages : en Pages : 530
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: Publisher: World Scientific ISBN: Category : Languages : en Pages : 1001
Author: Dan V. Voiculescu Publisher: European Mathematical Society ISBN: 9783037191651 Category : Free probability theory Languages : en Pages : 148
Book Description
Free probability is a probability theory dealing with variables having the highest degree of noncommutativity, an aspect found in many areas (quantum mechanics, free group algebras, random matrices, etc.). Thirty years after its foundation, it is a well-established and very active field of mathematics. Originating from Voiculescu's attempt to solve the free group factor problem in operator algebras, free probability has important connections with random matrix theory, combinatorics, harmonic analysis, representation theory of large groups, and wireless communication. These lecture notes arose from a master class in Munster, Germany and present the state of free probability from an operator algebraic perspective. This volume includes introductory lectures on random matrices and combinatorics of free probability (Speicher), free monotone transport (Shlyakhtenko), free group factors (Dykema), free convolution (Bercovici), easy quantum groups (Weber), and a historical review with an outlook (Voiculescu). To make it more accessible, the exposition features a chapter on the basics of free probability and exercises for each part. This book is aimed at master students to early career researchers familiar with basic notions and concepts from operator algebras.
Author: Jose Iovino Publisher: CRC Press ISBN: 042955866X Category : Mathematics Languages : en Pages : 596
Book Description
Model theory is the meta-mathematical study of the concept of mathematical truth. After Afred Tarski coined the term Theory of Models in the early 1950’s, it rapidly became one of the central most active branches of mathematical logic. In the last few decades, ideas that originated within model theory have provided powerful tools to solve problems in a variety of areas of classical mathematics, including algebra, combinatorics, geometry, number theory, and Banach space theory and operator theory. The two volumes of Beyond First Order Model Theory present the reader with a fairly comprehensive vista, rich in width and depth, of some of the most active areas of contemporary research in model theory beyond the realm of the classical first-order viewpoint. Each chapter is intended to serve both as an introduction to a current direction in model theory and as a presentation of results that are not available elsewhere. All the articles are written so that they can be studied independently of one another. This second volume contains introductions to real-valued logic and applications, abstract elementary classes and applications, interconnections between model theory and function spaces, nonstucture theory, and model theory of second-order logic. Features A coherent introduction to current trends in model theory. Contains articles by some of the most influential logicians of the last hundred years. No other publication brings these distinguished authors together. Suitable as a reference for advanced undergraduate, postgraduates, and researchers. Material presented in the book (e.g, abstract elementary classes, first-order logics with dependent sorts, and applications of infinitary logics in set theory) is not easily accessible in the current literature. The various chapters in the book can be studied independently.
Author: Daniel Redelmeier
Author: Daniel Redelmeier
Author: Kenneth Jay Dykema
Author: Dan V. Voiculescu
Author: 野水克己
Author: Source Wikipedia
Author: Bruce Blackadar
Author: 
Author: Dan V. Voiculescu
Author: Jose Iovino
Author: Nihon Sūgakkai