The Helton-Howe measure of almost normal Toeplitz operators
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866915784132919296 |
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| author | Sugahara, Yuto |
| author_facet | Sugahara, Yuto |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_07504 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Helton-Howe measure of almost normal Toeplitz operators Sugahara, Yuto Functional Analysis 47B35 (Primary) 47B10, 47A35 (Secondary) 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. |
| title | The Helton-Howe measure of almost normal Toeplitz operators |
| topic | Functional Analysis 47B35 (Primary) 47B10, 47A35 (Secondary) |
| url | https://arxiv.org/abs/2602.07504 |