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Operator theory --- 517.986 --- Hilbert space --- Morita duality --- Operator algebras --- Algebras, Operator --- Topological algebras --- Duality, Morita --- Morita's duality --- Modules (Algebra) --- Banach spaces --- Hyperspace --- Inner product spaces --- Topological algebras. Theory of infinite-dimensional representations --- 517.986 Topological algebras. Theory of infinite-dimensional representations --- Hilbert space. --- Morita duality. --- Hilbert, Espaces de --- Hilbert, Espaces de.

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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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Quantum groups --- 517.986 --- Enveloping algebras, Quantized --- Function algebras, Quantized --- Groups, Quantum --- Quantized enveloping algebras --- Quantized function algebras --- Quantum algebras --- Group theory --- Mathematical physics --- Quantum field theory --- 517.986 Topological algebras. Theory of infinite-dimensional representations --- Topological algebras. Theory of infinite-dimensional representations --- Quantum theory --- Théorie des groupes --- Théorie quantique

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Algebra --- 517.986 --- 517.984 --- C*-algebras --- Tensor products --- Products, Tensor --- Algebras, Linear --- Calculus of tensors --- Tensor algebra --- Algebras, C star --- Algebras, W star --- C star algebras --- W star algebras --- W*-algebras --- Banach algebras --- Topological algebras. Theory of infinite-dimensional representations --- Spectral theory of linear operators --- 517.984 Spectral theory of linear operators --- 517.986 Topological algebras. Theory of infinite-dimensional representations --- C*-algebras. --- Tensor products. --- Produits tensoriels --- C*-algèbres --- Produits tensoriels. --- C*-algèbres.