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Decomposition Theory

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Part of the Classics in Mathematics book series (CLASSICS, volume 60)

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 aâ (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.

Keywords

Hilbert Space Central Measure Radon Measure Polish Space Tracial State 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  1. 1.Department of MathematicsNihon UniversitySetagaya-Ku, Tokyo 156Japan

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