Invertibility of Bergman Toeplitz operators
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911203478994944 |
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| author | Javed, Mo Maji, Amit |
| author_facet | Javed, Mo Maji, Amit |
| contents | In this paper, we establish the invertibility of the Berezin transform of the symbol as a necessary and sufficient condition for the invertibility of the Toeplitz operator on the Bergman space $L^2_a(\mathbb{D})$. More precisely, if $ϕ = c g + d \bar{g}$, where $c,d\in\mathbb{C}$ and $g\in H^{\infty}(\mathbb{D})$, the space of all bounded analytic functions, then $T_ϕ$ is invertible on $L^2_a(\mathbb{D})$ if and only if $\inf\limits_{z\in \mathbb{D}}\left|\widetilde{\,ϕ}(z)\right|=\inf\limits_{z\in \mathbb{D}}|ϕ(z)|>0$, where $\widetilde{\,ϕ}$ is the Berezin transform of $ϕ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_09614 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Invertibility of Bergman Toeplitz operators Javed, Mo Maji, Amit Functional Analysis Complex Variables 47B35, 47A05, 30H20 In this paper, we establish the invertibility of the Berezin transform of the symbol as a necessary and sufficient condition for the invertibility of the Toeplitz operator on the Bergman space $L^2_a(\mathbb{D})$. More precisely, if $ϕ = c g + d \bar{g}$, where $c,d\in\mathbb{C}$ and $g\in H^{\infty}(\mathbb{D})$, the space of all bounded analytic functions, then $T_ϕ$ is invertible on $L^2_a(\mathbb{D})$ if and only if $\inf\limits_{z\in \mathbb{D}}\left|\widetilde{\,ϕ}(z)\right|=\inf\limits_{z\in \mathbb{D}}|ϕ(z)|>0$, where $\widetilde{\,ϕ}$ is the Berezin transform of $ϕ$. |
| title | Invertibility of Bergman Toeplitz operators |
| topic | Functional Analysis Complex Variables 47B35, 47A05, 30H20 |
| url | https://arxiv.org/abs/2510.09614 |