Continuous Tensor Products and Arveson’s Spectral C^{*}-Algebras.

Intro -- Contents -- 1 Introduction -- 2 Continuous Tensor Products -- 2.1 Tensor Decompositions over Boolean Algebras -- 2.1.1 Definition -- 2.1.2 Continuous Tensor Decompositions -- 2.1.3 Discrete Examples -- 2.1.4 Continuous Examples -- 2.2 The Generalized Araki-Woods Theorem -- 2.2.1 An Araki-Woods Theorem for B[sub(0)](I) -- 3 Algebras Associated to Continuous Tensor Products -- 3.1 Definition of L[sup(1)](T) and A(T) -- 3.1.1 L[sup(1)]-Sections as Involutive Banach Algebras -- 3.2 The C*-Algebra A{T) for T of Type I -- 3.2.1 Representations of A(T) -- 3.2.2 States -- 3.2.3 Ideals and Exact Sequences -- 3.3 Automorphisms and Endomorphisms -- 3.3.1 Ideal Preserving Automorphisms -- 3.3.2 General Diagonal Morphisms -- 3.3.3 Generation by Cones -- 3.3.4 Pedersen Ideal and Infiniteness -- 3.3.5 The Canonical Automorphic and Endomorphic Actions on A[sub(n)] -- 3.4 Homotopy Invariants -- 3.4.1 K-Theory -- 3.4.2 The Homotopy Type of the Automorphism Group -- 4 Arveson's Spectral C*-Algebras -- 4.1 Product Systems -- 4.1.1 E[sub(0)]-Semigroups and Product Systems -- 4.2 The Spectral C*-Algebra C*(E) of a Product System -- 4.2.1 The Wiener Hopf C*-Algebra -- 4.2.2 The Involutive Banach Algebra L[sup(1)] (K[sub(E)]) -- 4.2.3 C*(E) and its Universal Property -- 4.2.4 The C*-Algebras W[sub(n)] -- 4.3 C*(E[sub(n)]) as a Crossed Product -- 4.3.1 The Banach Algebra Crossed Product L[sup(1)] (R, L[sup(1)](T[sub(n)])) -- 4.3.2 Morita Equivalence between R [omitted] A[sub(n)] and C*(E[sub(n)]) -- 4.3.3 Simplicity -- 4.3.4 Infiniteness -- Appendix -- A. Bochner Integrals -- B. Direct Integrals -- C. Conditionally Positive Definite Functions -- References.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.