Bohr operator on opertor valued polyanalytic functions on simply connected domains

[2111.10883] Bohr operator on opertor valued polyanalytic functions on simply connected domains Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Complex Variables arXiv:2111.10883 (math) [Submitted on 21 Nov 2021 ( v1 ), last revised 24 Nov 2021 (this version, v2)] Title: Bohr operator on opertor valued polyanalytic functions on simply connected domains Authors: Vasudevarao Allu , Himadri Halder View a PDF of the paper titled Bohr operator on opertor valued polyanalytic functions on simply connected domains, by Vasudevarao Allu and Himadri Halder View PDF HTML (experimental) Abstract: In this article, we study the Bohr operator for the operator valued subordination class $S(f)$ consisting of holomorphic functions subordinate to $f$ in the unit disk $\mathbb{D}:=\{z \in \mathbb{C}: |z|<1\}$, where $f:\mathbb{D} \rightarrow \mathcal{B}(\mathcal{H})$ is holomorphic and $\mathcal{B}(\mathcal{H})$ is the algebra of bounded linear operators on a complex Hilbert space $\mathcal{H}$. We establish several subordination results, which can be viewed as the analogues of a couple of interesting subordination results from scalar valued settings. We also obtain a von Neumann-type inequality for the class of self-analytic mappings of the unit disk $\mathbb{D}$ which fix the origin. Furthermore, we extensively study Bohr inequalities for operator valued polyanalytic functions in certain proper simply connected domains in $\mathbb{C}$. We obtain Bohr radius for the operator valued polyanalytic functions of the form $F(z)= \sum_{l=0}^{p-1} \overline{z}^l \, f_{l}(z) $, where $f_{0}$ is subordinate to an operator valued convex biholomorphic function, and operator valued starlike biholomorphic function in the unit disk $\mathbb{D}$. Comments: We revise the proofs of Theorem 3.1, Theorem 3.2, and Theorem 3.3 in this article. 11 pages Subjects: Complex Variables (math.CV) ; Functional Analysis (math.FA) MSC classes: 30A10, 30B10, 30C50, 30C55, 30C62, 30F45, 30H30, 31A05, 30C20, 30C65 Cite as: arXiv:2111.10883 [math.CV] (or arXiv:2111.10883v2 [math.CV] for this version) https://doi.org/10.48550/arXiv.2111.10883 Focus to learn more arXiv-issued DOI via DataCite Journal reference: Canadian Mathematical Bulletin 66 (2023), 1411-1422 Related DOI : https://doi.org/10.4153/S0008439523000541 Focus to learn more DOI(s) linking to related resources Submission history From: Himadri Halder [ view email ] [v1] Sun, 21 Nov 2021 19:37:55 UTC (18 KB) [v2] Wed, 24 Nov 2021 13:54:50 UTC (18 KB) Full-text links: Access Paper: View a PDF of the paper titled Bohr operator on opertor valued polyanalytic functions on simply connected domains, by Vasudevarao Allu and Himadri Halder View PDF HTML (experimental) TeX Source view license Current browse context: math.CV < prev | next > new | recent | 2021-11 Change to browse by: math math.FA References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... 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