Turkish Journal of MathematicsInduced Mappings on Boolean Algebras of Clopen Sets and on Projections of the C*-Algebra C(X)
Department of Mathematics and Statistics
Jordan University of Science and Technology
Irbid 22110 JORDAN
Department of Mathematics
The Hashemite university
Abstract: For a compact space X, any group automorphism j of C(X,S1) induces a mapping Q on the Boolean algebra of the clopen subsets of X. We prove that the disjointness of Q equivalent to qj is an orthoisomorphism on the sets of projections of the C*-algebra C(X), when j(-1)=-1. Indeed, Q is a Boolean isomorphism iff qj preserves the product of projections. If X is equipped with a probability measure m, on a certain s-algebra of X, we show (under some condition) that Q preserves the disjoint of clopen subsets, up to sets of measure zero, or equivalently, the mapping qj is m-orthoisomorphism on the projections of the C*-algebra C(X).
Key Words: Unitary, Projections, Almost Isomorphisms, Boolean Algebra, Clopen Subset
Turk. J. Math., 31, (2007), 439-451.
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Other articles published in the same issue: Turk. J. Math.,vol.31,iss.4.