CROSSED-PRODUCTS BY SEMIGROUPS OF ENDOMORPHISMS AND THE TOEPLITZ ALGEBRAS OF ORDERED-GROUPS

Let Gamma(+) be the positive cone in a totally ordered abelian group G amma. We construct crossed products by actions of Gamma(+) as endomorp hisms of C-algebras, and give criteria which ensure a given represent ation of the crossed product is faithful. We use this to prove that th e C-algebras generated by two semigroups V, W : Gamma(+) --> B(H) of nonunitary isometries are canonically isomorphic, thus giving a new, s elf-contained proof of a theorem of Murphy, which includes earlier res ults of Coburn and Douglas.