For a compact space X, any group automorphism ψ of C(X,double struk D sign1) induces a mapping Θ on the Boolean algebra of the clopen subsets of X. We prove that the disjointness of Θ equivalent to θψ, is an orthoisomorphism on the sets of projections of the C*-algebra C(X), when ψ(-1) = -1. Indeed, Θ is a Boolean isomorphism iff θψ preserves the product of projections. If X is equipped with a probability measure μ, on a certain σ-algebra of X, we show (under some condition) that Θ preserves the disjoint of clopen subsets, up to sets of measure zero, or equivalently, the mapping θψ is μ-orthoisomorphism on the projections of the C*-algebra C(X).
|Number of pages||13|
|Journal||Turkish Journal of Mathematics|
|Publication status||Published - Dec 1 2007|
- Almost isomorphisms
- Boolean algebra
- Clopen subset
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