Abstract
For a compact space X, any group automorphism phi of C(X,S-1) induces a mappin Theta on the Boolean algebra of the clopen subsets of X. We, prove that the disjointness of Theta equivalent to theta(phi), is an orthoisomorphism on the sets of projections of the C*-algebra C(X), when phi(-1) = -1. Indeed, Theta is a Boolean isomorphism iff Theta, preserves the product of projections. If X is equipped with a probability measure p, on a certain sigma-algebra of X, we show (under some condition) that 8 preserves the disjoint of clopen subsets, up to sets of measure zero, or equivalently, the mapping theta(phi) is 1,mu-orthoisomorphism on the projections of the C*-algebra C(X).