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46l05 (primary)

Bulletin of the London Mathematical Society (1)

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EXTENSIONS OF BOHR'S INEQUALITY
VERN I. PAULSEN, DINESH SINGH
Journal:

Bulletin of the London Mathematical Society / Volume 38 / Issue 6 / December 2006

Published online by Cambridge University Press:

19 December 2006, pp. 991-999

Print publication:

December 2006
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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.