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A characterization of Banach spaces with nonzero Bohr radius

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Abstract

We obtain a necessary and sufficient condition for the occurrence of the Bohr phenomenon for Banach space valued analytic functions defined on the open unit disk \({{\mathbb {D}}}\). We also discuss its interesting consequences, which include the connection of the Bohr phenomenon with the strong maximum modulus principle, as well as some more specific criteria regarding the existence of nonzero Bohr radii for certain Banach spaces.

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Acknowledgements

The authors are thankful to the anonymous referee for his/her comments, which helped to improve the quality and presentation of this article.

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  1. Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, 721302, India

    Bappaditya Bhowmik & Nilanjan Das

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  1. Bappaditya Bhowmik
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  2. Nilanjan Das
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Bappaditya Bhowmik would like to thank SERB, DST, India (Ref No.-MTR/2018/001176) for its financial support through MATRICS grant.

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Bhowmik, B., Das, N. A characterization of Banach spaces with nonzero Bohr radius. Arch. Math. 116, 551–558 (2021). https://doi.org/10.1007/s00013-020-01568-8

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