03472nam 2200589 450 991048099140332120170822144439.01-4704-0271-8(CKB)3360000000464864(EBL)3114535(SSID)ssj0000888857(PQKBManifestationID)11453149(PQKBTitleCode)TC0000888857(PQKBWorkID)10865680(PQKB)10005071(MiAaPQ)EBC3114535(PPN)195415647(EXLCZ)99336000000046486419991022h20002000 uy| 0engur|n|---|||||txtccrContinuous tensor products and Arveson's spectral C*-algebras /Joachim ZachariasProvidence, Rhode Island :American Mathematical Society,[2000]©20001 online resource (118 p.)Memoirs of the American Mathematical Society,0065-9266 ;number 680"January 2000, volume 143, number 680 (second of 4 numbers)."0-8218-1545-8 Includes bibliographical references (pages 115-118).""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*â€?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""Memoirs of the American Mathematical Society ;no. 680.C*-algebrasTensor productsElectronic books.C*-algebras.Tensor products.510 s512/.55Zacharias Joachim1966-935568MiAaPQMiAaPQMiAaPQBOOK9910480991403321-algebras2513405UNINA