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Subfactors have been a subject of considerable research activity for about fifteen years and are known to have significant relations with other fields such as low dimensional topology and algebraic quantum field theory. These notes give an introduction to the subject suitable for a student who has only a little familiarity with the theory of Hilbert space. A new pictorial approach to subfactors is presented in a late chapter.

Operator algebras. --- Algebras, Operator --- Operator theory --- Topological algebras

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Fundamentals of the theory of operator algebras. V4

Operator algebras. --- Operator theory. --- Functional analysis --- Algebras, Operator --- Operator theory --- Topological algebras

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The theory of operator algebras is generally considered over the field of complex numbers and in the complex Hilbert spaces. So it is a natural and interesting problem: How is the theory in the field of real numbers? Up to now, the theory of operator algebras over the field of real numbers has seemed not to be introduced systematically and sufficiently.The aim of this book is to set up the fundamentals of real operator algebras and to give a systematic discussion for real operator algebras. Since the treatment is from the beginning (real Banach and Hilbert spaces, real Banach algebras, real Ba

Banach algebras. --- Operator algebras. --- Algebras, Operator --- Operator theory --- Topological algebras --- Algebras, Banach --- Banach rings --- Metric rings --- Normed rings --- Banach spaces

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Historically, operator theory and representation theory both originated with the advent of quantum mechanics. The interplay between the subjects has been and still is active in a variety of areas.This volume focuses on representations of the universal enveloping algebra, covariant representations in general, and infinite-dimensional Lie algebras in particular. It also provides new applications of recent results on integrability of finite-dimensional Lie algebras. As a central theme, it is shown that a number of recent developments in operator algebras may be handled in a particularly e

Operator algebras. --- Representations of algebras. --- Algèbres d'opérateurs --- Représentations d'algèbres --- Operator algebras --- Representations of algebras --- Algebra --- Algebras, Operator --- Operator theory --- Topological algebras

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In this book, first published in 2003, the reader is provided with a tour of the principal results and ideas in the theories of completely positive maps, completely bounded maps, dilation theory, operator spaces and operator algebras, together with some of their main applications. The author assumes only that the reader has a basic background in functional analysis, and the presentation is self-contained and paced appropriately for graduate students new to the subject. Experts will also want this book for their library since the author illustrates the power of methods he has developed with new and simpler proofs of some of the major results in the area, many of which have not appeared earlier in the literature. An indispensable introduction to the theory of operator spaces for all who want to know more.

Operator algebras. --- Dilation theory (Operator theory) --- Mappings (Mathematics) --- Maps (Mathematics) --- Functions --- Functions, Continuous --- Topology --- Transformations (Mathematics) --- Operator theory --- Algebras, Operator --- Topological algebras