A characterization of Banach spaces with nonzero Bohr radius

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.