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Bohr phenomenon for operator-valued functions

Part of: Series expansions Geometric function theory General theory of linear operators

Published online by Cambridge University Press:  08 January 2021

Bappaditya Bhowmik  and
Nilanjan Das
Bappaditya Bhowmik
Affiliation:
Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur721302, India (bappaditya@maths.iitkgp.ac.in; nilanjan@iitkgp.ac.in)
Nilanjan Das
Affiliation:
Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur721302, India (bappaditya@maths.iitkgp.ac.in; nilanjan@iitkgp.ac.in)
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Abstract

We establish Bohr inequalities for operator-valued functions, which can be viewed as analogues of a couple of interesting results from scalar-valued settings. Some results of this paper are motivated by the classical flavour of Bohr inequality, while others are based on a generalized concept of the Bohr radius problem.

Keywords

Bohr radiusharmonic functionbiholomorphic function

MSC classification

Primary: 47A56: Functions whose values are linear operators (operator and matrix valued functions, etc., including analytic and meromorphic ones) 30B10: Power series (including lacunary series) 47A63: Operator inequalities 30C80: Maximum principle; Schwarz's lemma, Lindelöf principle, analogues and generalizations; subordination
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 64 , Issue 1 , February 2021 , pp. 72 - 86
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Copyright
Copyright © The Author(s) 2021. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society

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