The Index Theory Associated to a Non-Finite Trace on a C*-Algebra

Abstract

AbstractThe index theory considered in this paper, a generalisation of the classical Fredholm index theory, is obtained in terms of a non-finite trace on a unitalC*-algebra. We relate it to the index theory of M. Breuer, which is developed in a von Neumann algebra setting, by means of a representation theorem. We show how our new index theory can be used to obtain an index theorem for Toeplitz operators on the compact group U(2), where the classical index theory does not give any interesting result.