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 As of A may be order-isomorphically embedded into the real Banach space C r (L) of all real valued continuous functions on L.
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© 1998 Springer-Verlag Berlin Heidelberg
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Sakai, S. (1998). Decomposition Theory. In: C*-Algebras and W*-Algebras. Classics in Mathematics, vol 60. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61993-9_3
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DOI: https://doi.org/10.1007/978-3-642-61993-9_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-63633-5
Online ISBN: 978-3-642-61993-9
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