Turkish Journal of Mathematics

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 q_j 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 q_j 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 q_j is m-orthoisomorphism on the projections of the C^*-algebra C(X).

Key Words: Unitary, Projections, Almost Isomorphisms, Boolean Algebra, Clopen Subset