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发表于 2025-3-21 21:49:36
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发表于 2025-3-22 02:38:10
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 .) Finall
流浪
发表于 2025-3-22 05:40:38
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
发表于 2025-3-22 08:42:45
Dynamical Correspondencesespondence of observables and generators of one-parameter groups of automorphisms in quantum mechanics. It is closely related to Connes’ concept of orientation that he used as a key property in his characterization of the natural self-dual cones associated with von Neumann alge
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发表于 2025-3-22 15:36:12
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
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发表于 2025-3-22 21:00:57
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易于
发表于 2025-3-22 21:56:15
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
纹章
发表于 2025-3-23 04:55:30
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 characterization 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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发表于 2025-3-23 06:28:39
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