The Helton-Howe measure of almost normal Toeplitz operators

Abstract

The Helton-Howe measure associated with an almost normal operator was constructed by Helton and Howe. It provides a trace formula that allows us to calculate the trace of commutators that would otherwise be incalculable. We will investigate almost normal Toeplitz operators and determine their Helton-Howe measures in terms of the harmonic extensions of the symbols. Our result may be thought of as a generalization of the winding number formula of the Fredholm index of a Toeplitz operator.