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Informationen zum Autor Nik Weaver Klappentext With a unique approach and presenting an array of new and intriguing topics, Mathematical Quantization offers a survey of operator algebras and related structures from the point of view that these objects are quantizations of classical mathematical structures. This approach makes possible, with minimal mathematical detail, a unified treatment of a variety of topics.Detailed here for the first time, the fundamental idea of mathematical quantization is that sets are replaced by Hilbert spaces. Building on this idea, and most importantly on the fact that scalar-valued functions on a set correspond to operators on a Hilbert space, one can determine quantum analogs of a variety of classical structures. In particular, because topologies and measure classes on a set can be treated in terms of scalar-valued functions, we can transfer these constructions to the quantum realm, giving rise to C*- and von Neumann algebras.In the first half of the book, the author quickly builds the operator algebra setting. He uses this as a unifying theme in the second half, in which he treats several active research topics, some for the first time in book form. These include the quantum plane and tori, operator spaces, Hilbert modules, Lipschitz algebras, and quantum groups.For graduate students, Mathematical Quantization offers an ideal introduction to a research area of great current interest. For professionals in operator algebras and functional analysis, it provides a readable tour of the current state of the field. Zusammenfassung Presenting an array of new topics, "Mathematical Quantization" explores operator algebras. For graduate students, this text offers an introduction to a large area of active research, and for professionals in operating algebras and functional analysis, it provides a tour of the field. Inhaltsverzeichnis QUANTUM MECHANICSClassical PhysicsStates and EventsObservablesDynamicsComposite SystemsQuantum ComputationHILBERT SPACESDefinitions and ExamplesSubspacesOrthonormal BasesDuals and Direct SumsTensor ProductsQuantum LogicOPERATORSUnitaries and ProjectionsContinuous Functional CalculusBorel Functional CalculusSpectral MeasuresThe Bounded Spectral TheoremUnbounded OperatorsThe Unbounded Spectral TheoremStone's TheoremTHE QUANTUM PLANEPosition and MomentumThe Tracial RepresentationBargmann-Segal SpaceQuantum Complex AnalysisC*-ALGEBRASThe Algebras C(X)Topologies from FunctionsAbelian C*-AlgebrasThe Quantum PlaneQuantum ToriThe GNS ConstructionVON NEUMANN ALGEBRASThe Algebras l8 (X)The Algebras L8 (X)Trace Class OperatorsThe Algebras B(H)Von Neumann AlgebrasThe Quantum Plane and ToriQUANTUM FIELD THEORYFock SpaceCCR AlgebrasRealtivistic ParticlesFlat SpacetimeCurved SpacetimeOPERATOR SPACESThe Spaces V(K)Mstiex Norms and ConvexityDualityMatrix-Valued FunctionsOperator SystemsHILBERT MODULESContinuous Hilbert BundlesHilbert L8-ModulesHilber C*-ModulesHilbert W*-ModulesCrossed ProductsHilbert *-BimodulesLIPSCHITZ ALGEBRASThe Algebras Lip0(X)Measurable MetricsThe Derivation TheoremExamplesQuantum Markov SemigroupsQUANTUM GROUPSFinite Dimensional C*-AlgebrasFinite Quantum GroupsCompact Quantum GroupsHaar Measure\REFERENCES ...
