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- W2079651923 abstract "Let (A, G, a) be a C*-dynamical system, namely a triple consisting of a C*algebra A, a locally compact group G and a homomorphism a from G into the automorphism group of A such that G3t-+ oct(x)EA is continuous for each x in A. Now assume that the C*-algebra A is unital. Then the set of a-invariant states of A, denoted by S, forms a weak* compact convex subset in the state space of A, and each extremal point in S is called an ergodic state (occasionally, G-ergodic state or oc-ergodic state). When we attempt to decompose an ainvariant state into ergodic states, it is most important to investigate the existence and uniqueness of the decomposition, and in order to carry out such investigation we need to require some abelianness of C* -dynamical systems, in particular, of invariant states. Now denote by (nv, u , H^, <^) the GNS covariant representation associated with an a-invariant state <p, that is, n^ is a representation of A on the Hilbert space Hv with the canonical cyclic vector <^ and u is a strongly continuous unitary representation of G on Hv defined by «?KW)^ = ^(«tM)^ for xeA and teG. Note that" @default.
- W2079651923 created "2016-06-24" @default.
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- W2079651923 date "1990-01-01" @default.
- W2079651923 modified "2023-10-18" @default.
- W2079651923 title "{$G$}-central states of almost periodic type on {$Csp *$}-algebras" @default.
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- W2079651923 doi "https://doi.org/10.2977/prims/1195170573" @default.
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