Induced mappings on boolean algebras of clopen sets and on projections of the C*-algebra C(X)

Ahmed Al-Rawashdeh, Wasfi Shatanawi

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1 Citation (Scopus)

Abstract

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).

Original languageEnglish
Pages (from-to)439-451
Number of pages13
JournalTurkish Journal of Mathematics
Volume31
Issue number4
Publication statusPublished - Dec 2007
Externally publishedYes

Keywords

  • Almost isomorphisms
  • Boolean algebra
  • Clopen subset
  • Projections
  • Unitary

ASJC Scopus subject areas

  • General Mathematics

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