Turkish Journal of Mathematics
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 \sigma-algebra 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 \mu-orthoisomorphism 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
AL-RAWASHDEH, 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
