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Extensions of Bohr'S Inequality
Author(s) -
Paulsen Vern I.,
Singh Dinesh
Publication year - 2006
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609306019084
Subject(s) - bohr model , mathematics , bounded function , pure mathematics , scalar (mathematics) , inequality , bohr radius , mathematics subject classification , mathematical analysis , quantum mechanics , geometry , physics , quantum dot
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 D, and to bounded analytic functions on the annulus. 2000 Mathematics Subject Classification 46L05 (primary), 46A22, 46H25, 46M10, 47A20 (secondary).