Bounded Toeplitz Products on the Hardy Space
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916588596232192 |
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| author | O'Loughlin, Ryan |
| author_facet | O'Loughlin, Ryan |
| contents | A Toeplitz operator on the Hardy space of the unit circle is bounded if and only if its symbol is bounded. For two Toeplitz operators, there are no known function-theoretic conditions for their symbols, which are equivalent to the product of the Toeplitz operators being bounded. In this paper, we provide a solution to this problem, by showing under certain assumptions that the product of two Toeplitz operators is bounded if and only if the product of their symbols is bounded. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_14069 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bounded Toeplitz Products on the Hardy Space O'Loughlin, Ryan Functional Analysis 47B35, 30H10, 47B48 A Toeplitz operator on the Hardy space of the unit circle is bounded if and only if its symbol is bounded. For two Toeplitz operators, there are no known function-theoretic conditions for their symbols, which are equivalent to the product of the Toeplitz operators being bounded. In this paper, we provide a solution to this problem, by showing under certain assumptions that the product of two Toeplitz operators is bounded if and only if the product of their symbols is bounded. |
| title | Bounded Toeplitz Products on the Hardy Space |
| topic | Functional Analysis 47B35, 30H10, 47B48 |
| url | https://arxiv.org/abs/2501.14069 |