The Helton-Howe measure of almost normal Toeplitz operators
Functional Analysis
2026-02-10 v1
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.
Keywords
Cite
@article{arxiv.2602.07504,
title = {The Helton-Howe measure of almost normal Toeplitz operators},
author = {Yuto Sugahara},
journal= {arXiv preprint arXiv:2602.07504},
year = {2026}
}
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16 pages