Decomposition Theory

Abstract

Let A be a C*-algebra with identity, (in this section, we shall always assume that a C*-algebra A has an identity), A* the dual of A, and let L be the state space, with the topology σ(L,A), of A. Let C(L) be the Banach algebra of all complex valued continuous functions on the compact space L with the usual supremum norm. For a∈A, a function â on L is defined by â(φ) = φ(a) (φ∈L). By the mapping a→â (A) the A may be topologically embedded into C(L); moreover the self-adjoint portion A^s of A may be order-isomorphically embedded into the real Banach space C _r (L) of all real valued continuous functions on L.