Journal of Operator Theory

Volume 95, Issue 2, Spring 2026 pp. 481-503.

On multidimensional Bohr radii for Banach spaces

Authors: Vasudevarao All (1), Subhadip Pal (2)
Author institution: (1) Department of Mathematics,School of Basic Sciences, Indian Institute of Technology Bhubaneswar, Bhubaneswar-752050, Odisha, India
(2) Department of Mathematics, School of Basic Sciences, Indian Institute of Technology Bhubaneswar, Bhubaneswar-752050, Odisha, India

Summary: In this paper, we study a more general version of multidimensional Bohr radii for the holomorphic functions defined on unit ball of $\ell^n_q\,\,(1\leqslant q\leqslant \infty)$ spaces with values in arbitrary complex Banach spaces. More precisely, we study the multidimensional Bohr radii for bounded linear operators between complex Banach spaces, primarily motivated by the work of A. Defant, M. Maestre, and U. Schwarting (\textit{Adv. Math.} 231(2012), pp.\ 2837--2857). We obtain the exact asymptotic estimates of multidimensional Bohr radius for both finite and infinite dimensional Banach spaces. As an application, we find the lower bound of arithmetic Bohr radius.

DOI: http://dx.doi.org/10.7900/jot.2024jul01.249
Keywords: Bohr radius, power series, holomorphic functions, homogeneous polynomials, Banach spaces

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