A counterexample of the Fredholm of Toeplitz operator
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915191742005248 |
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| author | Liu, Hua Zhang, Xinyang |
| author_facet | Liu, Hua Zhang, Xinyang |
| contents | In this paper we study the essential spectra of the Toeplitz operator on the Hardy space $H^1$. We give a counterexample to show that the Toeplitz operator with symbol is not Fredholm, which gives a counterexample to the conjecture by J.A. Virtanen J A in 2006. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_08590 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A counterexample of the Fredholm of Toeplitz operator Liu, Hua Zhang, Xinyang Functional Analysis Complex Variables In this paper we study the essential spectra of the Toeplitz operator on the Hardy space $H^1$. We give a counterexample to show that the Toeplitz operator with symbol is not Fredholm, which gives a counterexample to the conjecture by J.A. Virtanen J A in 2006. |
| title | A counterexample of the Fredholm of Toeplitz operator |
| topic | Functional Analysis Complex Variables |
| url | https://arxiv.org/abs/2503.08590 |