$G$-Central States of Almost Periodic Type on $C^*$-Algebras | Zendy

Masaharu Kusuda | Zendy

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$G$-Central States of Almost Periodic Type on $C^*$-Algebras

Author(s) -

Masaharu Kusuda

Publication year - 1990

Publication title -

publications of the research institute for mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.786

H-Index - 39

eISSN - 1663-4926

pISSN - 0034-5318

DOI - 10.2977/prims/1195170573

Subject(s) - mathematics , ergodic theory , invariant (physics) , bijection , unitary representation , hilbert space , covariant transformation , automorphism , combinatorics , homomorphism , locally compact space , pure mathematics , state (computer science) , discrete mathematics , lie group , mathematical physics , algorithm

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

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