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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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Operator algebras --- Algebras, Operator --- Operator theory --- Topological algebras --- Algebraic topology
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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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Fundamentals of the theory of operator algebras. V2
Operator algebras. --- Linear operators. --- Linear maps --- Maps, Linear --- Operators, Linear --- Operator theory --- Algebras, Operator --- 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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This book consists of research papers that cover the scientific areas of the International Workshop on Operator Theory, Operator Algebras and Applications, held in Lisbon in September 2012. The volume particularly focuses on (i) operator theory and harmonic analysis (singular integral operators with shifts; pseudodifferential operators, factorization of almost periodic matrix functions; inequalities; Cauchy type integrals; maximal and singular operators on generalized Orlicz-Morrey spaces; the Riesz potential operator; modification of Hadamard fractional integro-differentiation), (ii) operator algebras (invertibility in groupoid C*-algebras; inner endomorphisms of some semi group, crossed products; C*-algebras generated by mappings which have finite orbits; Folner sequences in operator algebras; arithmetic aspect of C*_r SL(2); C*-algebras of singular integral operators; algebras of operator sequences) and (iii) mathematical physics (operator approach to diffraction from polygonal-conical screens; Poisson geometry of difference Lax operators).
Operator theory. --- Operator algebras. --- Functional analysis --- Algebras, Operator --- Operator theory --- Topological algebras --- Differential equations, partial. --- Partial Differential Equations. --- Operator Theory. --- Partial differential equations --- Partial differential equations.
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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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About four years ago a prominent string theorist was quoted as saying that it might be possible to understand quantum mechanics by the year 2000. Sometimes new mathematical developments make such understanding appear possible and even close, but on the other hand, increasing lack of experimental verification make it seem to be further distant. In any event one seems to arrive at new revolutions in physics and mathematics every year. This book hopes to convey some of the excitment of this period, but will adopt a relatively pedestrian approach designed to illuminate the relations between qua
Geometric quantization. --- Operator algebras. --- Mathematical physics. --- Physical mathematics --- Physics --- Algebras, Operator --- Operator theory --- Topological algebras --- Geometry, Quantum --- Quantization, Geometric --- Quantum geometry --- Geometry, Differential --- Quantum theory --- Mathematics
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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
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Operator theory --- Analytical spaces --- Algebraic topology --- Operator algebras --- K-theory --- 517.986 --- Algebras, Operator --- Topological algebras --- Homology theory --- Topological algebras. Theory of infinite-dimensional representations --- 517.986 Topological algebras. Theory of infinite-dimensional representations
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