Описание: Algebras of bounded operators are familiar, either as C*-algebras or as von Neumann algebras. A first generalization is the notion of algebras of unbounded operators (O*-algebras), mostly developed by the Leipzig school and in Japan (for a review, we refer to the monographs of K. SchmГјdgen  and A. Inoue ). This volume goes one step further, by considering systematically partial *-algebras of unbounded operators (partial O*-algebras) and the underlying algebraic structure, namely, partial *-algebras. It is the first textbook on this topic. The first part is devoted to partial O*-algebras, basic properties, examples, topologies on them. The climax is the generalization to this new framework of the celebrated modular theory of Tomita-Takesaki, one of the cornerstones for the applications to statistical physics. The second part focuses on abstract partial *-algebras and their representation theory, obtaining again generalizations of familiar theorems (Radon-Nikodym, Lebesgue).
Автор: Bratteli Название: Operator Algebras ISBN: 354034196X ISBN-13(EAN): 9783540341963 Издательство: Springer Рейтинг: Цена: 19056 р. Наличие на складе: Поставка под заказ.
Описание: The theme of the first Abel Symposium was operator algebras in a wide sense. In the last 40 years operator algebras have developed from a rather special discipline within functional analysis to become a central field in mathematics often described as non-commutative geometry (see for example the book "Non-Commutative Geometry" by the Fields medalist Alain Connes). It has branched out in several subdisciplines and made contact with other subjects like for example mathematical physics, algebraic topology, geometry, dynamical systems, knot theory, ergodic theory, wavelets, representations of groups and quantum groups. Norway has a relatively strong group of researchers in the subject, which contributed to the award of the first symposium in the series of Abel Symposia to this group. The contributions to this volume give a state-of-the-art account of some of these subdisciplines.
Описание: Contains three survey lecture courses and 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. This title reflects developments in the area of operator algebras.
Автор: Gerald J. Murphy Название: C*-Algebras and Operator Theory, ISBN: 0125113609 ISBN-13(EAN): 9780125113601 Издательство: Elsevier Science Рейтинг: Цена: 6693 р. Наличие на складе: Поставка под заказ.
Описание: This book constitutes a first- or second-year graduate course in operator theory. It is a field that affects other areas of mathematics and physics, such as algebraic topology, differential geometry and quantum mechanics.
Автор: Takesaki Masamichi Название: Theory of Operator Algebras II ISBN: 354042914X ISBN-13(EAN): 9783540429142 Издательство: Springer Рейтинг: Цена: 16169 р. Наличие на складе: Поставка под заказ.
Описание: Together with "Theory of Operator Algebras I, III" (EMS 124 and 127), this book, written by one of the most prominent researchers in the field of operator algebras, presents the theory of von Neumann algebras and non-commutative integration focusing on the group of automorphisms and the structure analysis. It is part of the recently developed part of the "Encyclopaedia of Mathematical Sciences" on operator algebras and non-commutative geometry (see http://www.springer.de/math/ems/index.html). The book provides essential and comprehensive information for graduate students and researchers in mathematics and mathematical physics.
Автор: Takesaki M. Название: Theory of Operator Algebras I ISBN: 354042248X ISBN-13(EAN): 9783540422488 Издательство: Springer Рейтинг: Цена: 17324 р. Наличие на складе: Поставка под заказ.
Описание: Since its inception by von Neumann 70 years ago, the theory of operator algebras has become a rapidly developing area of importance for the understanding of many areas of mathematics and theoretical physics. Accessible to the non-specialist, this first part of a three volume treatise provides a clear, carefully written survey that emphasizes the theory's analytical and topological aspects.The book's unifying theme is the Banach space duality for operator algebras. This allows the reader to recognize the affinity between operator algebras and measure theory on locally compact spaces. Very technical sections are clearly labeled and there are extensive comments by the author, a good historical background and excercises.This book is part of the subseries of the EMS on Operator Algebras and Non-Commutative Geometry.
Автор: Takesaki Masamichi Название: Theory of Operator Algebras III ISBN: 3540429131 ISBN-13(EAN): 9783540429135 Издательство: Springer Рейтинг: Цена: 16169 р. Наличие на складе: Поставка под заказ.
Описание: Together with "Theory of Operator Algebras I, II" (EMS 124 and 125), this book, written by one of the most prominent researchers in the field of operator algebras, presents the theory of von Neumann algebras and non-commutative integration focusing on the group of automorphisms and the structure analysis. It is is part of the recently developed part of the "Encyclopaedia of Mathematical Sciences" on operator algebras and non-commutative geometry (see http://www.springer.de/math/ems/index.html). The book provides essential and comprehensive information for graduate students and researchers in mathematics and mathematical physics.
Описание: This book consists of a careful selection of peer-reviewed articles originating from the 19th International Conference on Operator Theory, held in Timisoara in
Summer 2002. It contains recent developments covering a broad range of topics from operator theory, operator algebras and their applications, particularly to differential analysis,
complex functions, ergodic theory, mathematical physics, matrix analysis, and systems theory.
Описание: This work is motivated by and develops connections between several branches of mathematics and physics--the theories of Lie algebras, finite groups and modular functions in mathematics, and string theory in physics. The first part of the book presents a new mathematical theory of vertex operator algebras, the algebraic counterpart of two-dimensional holomorphic conformal quantum field theory. The remaining part constructs the Monster finite simple group as the automorphism group of a very special vertex operator algebra, called the "moonshine module" because of its relevance to "monstrous moonshine."
Автор: Ola Bratteli; Sergey Neshveyev; Christian Skau Название: Operator Algebras ISBN: 3642070612 ISBN-13(EAN): 9783642070617 Издательство: Springer Рейтинг: Цена: 19056 р. Наличие на складе: Поставка под заказ.
Описание: The theme of the first Abel Symposium was operator algebras in a wide sense. This is the first volume in a prestigious new book series linked to the Abel prize. The contributions give a state-of-the-art account of some of the subject`s sub-disciplines.
Автор: Carlsen Название: Operator Algebras and Applications ISBN: 3319392840 ISBN-13(EAN): 9783319392844 Издательство: Springer Рейтинг: Цена: 16746 р. Наличие на складе: Поставка под заказ.
Описание: Like the first Abel Symposium, held in 2004, the Abel Symposium 2015 focused on operator algebras. It is interesting to see the remarkable advances that have been made in operator algebras over these years, which strikingly illustrate the vitality of the field. A total of 26 talks were given at the symposium on a variety of themes, all highlighting the richness of the subject.The field of operator algebras was created in the 1930s and was motivated by problems of quantum mechanics. It has subsequently developed well beyond its initial intended realm of applications and expanded into such diverse areas of mathematics as representation theory, dynamical systems, differential geometry, number theory and quantum algebra. One branch, known as “noncommutative geometry”, has become a powerful tool for studying phenomena that are beyond the reach of classical analysis.This volume includes research papers that present new results, surveys that discuss the development of a specific line of research, and articles that offer a combination of survey and research. These contributions provide a multifaceted portrait of beautiful mathematics that both newcomers to the field of operator algebras and seasoned researchers alike will appreciate.
Описание: This EMS volume consists of two parts, written by leading scientists in the field of operator algebras and non-commutative geometry. The first part, written by M.Rordam, is on Elliott's classification program for nuclear C*-algebras. The emphasis is on the work of Kirchberg and the spectacular results by Kirchberg and Phillips giving a nearly complete classification, in terms of K-theoretic invariants, in the purely infinite case. This part of the program is described with almost full proofs beginning with Kirchberg's tensor product theorems and Kirchberg's embedding theorem for exact C*-algebras. The classification of finite simple C*-algebras starting with AF-algebras, and continuing with AT- and AH-algebras is covered, but mostly without proofs. The second part, written by E.Stormer, is a survey of the theory of of noncommutative entropy of automorphisms of C*-algebras and von Neumann algebras from its initiation by Connes and Stormer in 1975 till 2001.
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