Turkish Journal of Mathematics
Article Title
Induced Mappings on Boolean Algebras of Clopen Sets and on Projections of the C^*Algebra C(X)
DOI

Abstract
For a compact space X, any group automorphism \varphi of C(X,S^1) induces a mapping \Theta on the Boolean algebra of the clopen subsets of X. We prove that the disjointness of \Theta equivalent to \theta_{\varphi} is an orthoisomorphism on the sets of projections of the C^*algebra C(X), when \varphi(1)=1. Indeed, \Theta is a Boolean isomorphism iff \theta_{\varphi} preserves the product of projections. If X is equipped with a probability measure \mu, on a certain \sigmaalgebra of X, we show (under some condition) that \Theta preserves the disjoint of clopen subsets, up to sets of measure zero, or equivalently, the mapping \theta_{\varphi} is \muorthoisomorphism on the projections of the C^*algebra C(X).
Keywords
Unitary, Projections, Almost Isomorphisms, Boolean Algebra, Clopen Subset
First Page
439
Last Page
451
Recommended Citation
ALRAWASHDEH, AHMED and SHATANAWI, WASFI (2007) "Induced Mappings on Boolean Algebras of Clopen Sets and on Projections of the C^*Algebra C(X)," Turkish Journal of Mathematics: Vol. 31: No. 4, Article 11. Available at: https://journals.tubitak.gov.tr/math/vol31/iss4/11