Generalizations of Bohr inequality for Hilbert space operators
type: Item
instance of: scholarly article
title: Generalizations of Bohr inequality for Hilbert space operators
zbMATH Open document ID: 1170.26008
author: P. Hemchote
author: Pattrawut Chansangiam
author: Praiboon Pantaragphong
published in: Journal of Mathematical Analysis and Applications
publication date: 2009-06-18T00:00:00Z
review text: Let \({\mathcal B}({\mathbb H})\) be the space of all bounded linear operators on a complex separable Hilbert space \({\mathbb H}.\) Bohr's inequality for Hilbert space operators asserts that, for \(A, B\in {\mathcal B}({\mathbb H})\) and \(p, q>1\) real numbers such that \(1/p+1/q=1,\) \[ |A+B|^2\leq p|A|^2+q|B|^2 \] with equality if and only if \(pA=qB.\) In this paper, a number of generalizations of Bohr's inequality for operators in \({\mathcal B}({\mathbb H})\) are established. Moreover, Bohr inequalities are extended to multiple operators and some related inequalities are obtained. For each inequality a necessary and sufficient condition for the equality case is determined. The results obtained in this paper generalize previous existing results in the literature.
Mathematics Subject Classification ID: 26D07
zbMATH DE Number: 5566253
zbMATH Keywords: Bohr inequality
zbMATH Keywords: Hilbert space operator
reviewed by: Sotiris K. Ntouyas
MaRDI profile type: Publication
full work available at URL: j.jmaa.2009.03.006
OpenAlex ID: W2018389523
cites work: Bohr's inequalities for Hilbert space operators
cites work: Non-commutative operator Bohr inequality
cites work: Q4205660
cites work: On the Bohr inequality of operators
DOI: 10.1016/J.JMAA.2009.03.006
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description: scientific article; zbMATH DE number 5566253