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EXTENSIONS OF BOHR'S INEQUALITY

Published online by Cambridge University Press:  19 December 2006

VERN I. PAULSEN  and
DINESH SINGH
VERN I. PAULSEN
Affiliation:
Department of Mathematics, University of Houston, Houston, TX 77204-3476, USAvern@math.uh.edu
DINESH SINGH
Affiliation:
Department of Mathematics, University of Delhi, New Delhi, Indiadinesh_singh@hotmail.com
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Abstract

We obtain operator-valued analogues of Bohr's inequality involving both the absolute values of operators and their norms, that when restricted to the scalar case imply the classical Bohr inequality. In the scalar case we extend Bohr's inequality to the case where one function is majorized by another function, to the Hardy space, $H^2(\mathbb{D})$, and to bounded analytic functions on the annulus.

Keywords

46L05 (primary)46A2246H2546M1047A20 (secondary)
Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 38 , Issue 6 , December 2006 , pp. 991 - 999
Copyright
The London Mathematical Society 2006

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