Titlebook: Geometry of State Spaces of Operator Algebras; Erik M. Alfsen,Frederic W. Shultz Textbook 2003 Springer Science+Business Media New York 20

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書目名稱Geometry of State Spaces of Operator Algebras讀者反饋學科排名

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Structure of JBW-algebrasay–von Neumann equivalence of projections in von Neumann algebras.) We will define the notion of type I and type I.JBW-algebras, and describe the classification of type I.JBW-factors. (For the sake of brevity, most of these results will be stated without proof, with references given to [67].) Finall

流浪

Representations of JB-algebrasat there is one crucial difference compared to the situation for C*- algebras: not every JB-algebra admits such a concrete representation. The “Gelfand–Naimark” type theorem (Theorem 4.19) states that there is a certain exceptional ideal, and modulo that ideal every JB-algebra admits a concrete repr

Immortal

Dynamical Correspondencesespondence of observables and generators of one-parameter groups of automorphisms in quantum mechanics. It is closely related to Connes’ concept of orientation [36, Definition 4.11] that he used as a key property in his characterization of the natural self-dual cones associated with von Neumann alge

Traumatic-Grief

General Compressions be strengthened to characterize the state spaces of Jordan and C.-algebras. The first part of this program is to establish a satisfactory spectral theory and functional calculus. Here the guiding idea is to replace projections.by “projective units”.P1 determined by “general compressions”.defined by

Traumatic-Grief

易于

Characterization of Normal State Spaces of von Neumann Algebrasl state spaces of JBW-factors of type I by geometric axioms, among those the Hilbert ball property by which the face generated by each pair of extreme points is a Hilbert ball. In the case of.these balls will be 3-dimensional (A 120), and this “3-ball property” is the single additional property we n

紋章

Characterization of C*-algebra State SpacesC.-algebras have an identity, but our characterization can easily be adapted for non-unital algebras). We will start with our previous charac-terization of state spaces of JB-algebras (Theorem 9.38). Then we will add two additional properties that characterize C.-state spaces among state spaces of J

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