C*-algebras and their automorphism groups. (English) Zbl 0416.46043

Pedersen, Gert K.

London Mathematical Society Monographs. 14. London - New York -San Francisco: Academic Press. X, 416 p. $ 60.00 (1979).

MSC:

46L10	General theory of von Neumann algebras
46-02	Research exposition (monographs, survey articles) pertaining to functional analysis
46L40	Automorphisms of selfadjoint operator algebras
46L51	Noncommutative measure and integration
46L53	Noncommutative probability and statistics
46L54	Free probability and free operator algebras
46L35	Classifications of \(C^*\)-algebras
22D25	\(C^*\)-algebras and \(W^*\)-algebras in relation to group representations
81T05	Axiomatic quantum field theory; operator algebras

Keywords:

automorphism groups; C*-algebras; non-commutative analogue of Borel spaces; Gelfand representation theorem; convexity; positive part; antisymmetric Riesz decomposition theorem; automatic continuity of *-homomorphisms; von Neumann bi-commutant theorem; Kaplansky density theorem; non-commutative Lusin’s theorem; Kadison’s transitivity theorem; representations; GNS-construction; cyclic representations; universal enveloping von Neumann algebra; pure states; Jocobson topology; Dauns-Hofmann theorem; Borel *-algebras; disintegration theory of states; weights; traces; type; crossed products; duality; spectral analysis; Arveson spectrum; essential spectrum of Connes; Tomita-Takesaki theory; Rieffel-Van Daele approach; classification of factors