Convexity of the Berezin range of operators on $\mathcal{H}_γ(\mathbb{D})$
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916768808697856 |
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| author | Maiti, Sandip Kumar Sahoo, Satyajit Chakraborty, Gorachand |
| author_facet | Maiti, Sandip Kumar Sahoo, Satyajit Chakraborty, Gorachand |
| contents | In this paper, we characterize the convexity of the Berezin range for finite-rank operators acting on the weighted Hardy space $\mathcal{H}_γ(\mathbb{D})$ over the unit disc $\mathbb{D}$. We provide a complete classification in terms of convexity for concrete operators. Additionally, we address dynamical properties of finite-rank operators on Hardy and Bergman spaces. Several illustrative examples are discussed to support our theoretical findings. Additionally, geometrical interpretations have also been employed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_24495 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Convexity of the Berezin range of operators on $\mathcal{H}_γ(\mathbb{D})$ Maiti, Sandip Kumar Sahoo, Satyajit Chakraborty, Gorachand Functional Analysis 47B32, 52A10 In this paper, we characterize the convexity of the Berezin range for finite-rank operators acting on the weighted Hardy space $\mathcal{H}_γ(\mathbb{D})$ over the unit disc $\mathbb{D}$. We provide a complete classification in terms of convexity for concrete operators. Additionally, we address dynamical properties of finite-rank operators on Hardy and Bergman spaces. Several illustrative examples are discussed to support our theoretical findings. Additionally, geometrical interpretations have also been employed. |
| title | Convexity of the Berezin range of operators on $\mathcal{H}_γ(\mathbb{D})$ |
| topic | Functional Analysis 47B32, 52A10 |
| url | https://arxiv.org/abs/2505.24495 |