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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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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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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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This volume is addressed to those who wish to apply the methods and results of the theory of topological algebras to a variety of disciplines, even though confronted by particular or less general forms. It may also be of interest to those who wish, from an entirely theoretical point of view, to see how far one can go beyond the classical framework of Banach algebras while still retaining substantial results.The need for such an extension of the standard theory of normed algebras has been apparent since the early days of the theory of topological algebras, most notably the locally conve

Functional analysis --- Topological algebras. --- Operator algebras. --- Topological algebras --- 517.986 --- 517.986 Topological algebras. Theory of infinite-dimensional representations --- Topological algebras. Theory of infinite-dimensional representations --- Algebras, Topological --- Linear topological spaces --- Rings (Algebra) --- Algebras, Operator --- Operator theory