A characterization of Banach spaces with nonzero Bohr radius

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 D . We also discuss its interesting consequences, which include the connection of the Bohr phenomenon with the strong maximum modulus prin...

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Bibliographic Details
Published in:Archiv der Mathematik 2021-05, Vol.116 (5), p.551-558
Main Authors: Bhowmik, Bappaditya, Das, Nilanjan
Format: Article
Language:English
Subjects:
Analytic functions
Banach spaces
Mathematics
Mathematics and Statistics
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Summary: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 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.
ISSN:0003-889X
1420-8938
DOI:10.1007/s00013-020-01568-8