Operator valued analogues of multidimensional refined Bohr's inequalities
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866912103235846144 |
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| author | Allu, Vasudevarao Biswas, Raju Mandal, Rajib |
| author_facet | Allu, Vasudevarao Biswas, Raju Mandal, Rajib |
| contents | Let $\mathcal{B}(\mathcal{H})$ denote the Banach algebra of all bounded linear operators acting on complex Hilbert spaces $\mathcal{H}$. In this paper, we first establish several sharply refined versions of Bohr's inequality analogues with operator valued functions in the class $\mathcal{B}(\mathbb{D}, \mathcal{B}(\mathcal{H}))$ of bounded analytic functions from the unit disk $\mathbb{D}$ to $\mathcal{B}(\mathcal{H})$ with $\sup_{|z|<1}\Vert f(z)\leq 1$ by utilizing a certain power of the function's norm. Additionally, we establish several multidimensional analogues of refined Bohr's inequalities by using operator valued functions in the complete circular domain $Ω\subset\mathbb{C}^n$. All of the results are sharp. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_01677 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Operator valued analogues of multidimensional refined Bohr's inequalities Allu, Vasudevarao Biswas, Raju Mandal, Rajib Complex Variables 32A05, 32A10, 47A56, 47A63, 30H05 Let $\mathcal{B}(\mathcal{H})$ denote the Banach algebra of all bounded linear operators acting on complex Hilbert spaces $\mathcal{H}$. In this paper, we first establish several sharply refined versions of Bohr's inequality analogues with operator valued functions in the class $\mathcal{B}(\mathbb{D}, \mathcal{B}(\mathcal{H}))$ of bounded analytic functions from the unit disk $\mathbb{D}$ to $\mathcal{B}(\mathcal{H})$ with $\sup_{|z|<1}\Vert f(z)\leq 1$ by utilizing a certain power of the function's norm. Additionally, we establish several multidimensional analogues of refined Bohr's inequalities by using operator valued functions in the complete circular domain $Ω\subset\mathbb{C}^n$. All of the results are sharp. |
| title | Operator valued analogues of multidimensional refined Bohr's inequalities |
| topic | Complex Variables 32A05, 32A10, 47A56, 47A63, 30H05 |
| url | https://arxiv.org/abs/2411.01677 |