Extended zeta-function residues on principal ideals
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929412858970112 |
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| author | Tian, Yongqiang Usachev, Alexandr |
| author_facet | Tian, Yongqiang Usachev, Alexandr |
| contents | We study extended zeta-function residues on principal ideals of compact operators and their connections with Dixmier traces. We establish a Lidskii-type formula for continuous singular traces on these ideals. Using this formula, we obtain a necessary and sufficient conditions for an arbitrary operator being Dixmier measurable. These conditions are expressed in terms of eigenvalues of an operator and an asymptotic of its zeta-function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_05296 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Extended zeta-function residues on principal ideals Tian, Yongqiang Usachev, Alexandr Functional Analysis We study extended zeta-function residues on principal ideals of compact operators and their connections with Dixmier traces. We establish a Lidskii-type formula for continuous singular traces on these ideals. Using this formula, we obtain a necessary and sufficient conditions for an arbitrary operator being Dixmier measurable. These conditions are expressed in terms of eigenvalues of an operator and an asymptotic of its zeta-function. |
| title | Extended zeta-function residues on principal ideals |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2407.05296 |