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arXiv · 2602.07504

The Helton-Howe measure of almost normal Toeplitz operators

Yuto Sugahara
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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.

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Yuto Sugahara. 2026-02-07. The Helton-Howe measure of almost normal Toeplitz operators. https://doi.org/10.1007/s44146-026-00263-4

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