Bohr's inequalities for Hilbert space operators
type: Item
instance of: scholarly article
title: Bohr's inequalities for Hilbert space operators
zbMATH Open document ID: 1108.26018
author: Wing-Sum Cheung
author: J. Pečarić
published in: Journal of Mathematical Analysis and Applications
publication date: 2006-11-15T00:00:00Z
review text: Let \(\mathbb{H}\) be a complex separable Hilbert space and \(B(\mathbb{H})\) the algebra of all bounded linear operators on \(\mathbb{H}\). For any \(X\in B( \mathbb{H}),\) write \(\left| X\right| =\left( X\ast X\right) ^{1/2}.\) The authors prove the following generalization of Bohr's inequality: for any \(A,B\in B(\mathbb{H})\) and any \(p,q\in \mathbb{R}\) with \(p>1\) and \(\frac{1}{p }+\frac{1}{q}=1,\) \(\left| A+B\right| ^{2}\leq p\left| A\right| ^{2}+q\left| B\right| ^{2}. \)
Mathematics Subject Classification ID: 26D20
zbMATH DE Number: 5072953
zbMATH Keywords: parallelogram law
reviewed by: Gheorghe Toader
MaRDI profile type: Publication
full work available at URL: j.jmaa.2005.10.046
OpenAlex ID: W2087603297
cites work: Q5508554
cites work: Q5545526
cites work: Q5816708
cites work: Q3905923
cites work: Non-commutative operator Bohr inequality
cites work: Analytic Inequalities
cites work: Q4001361
cites work: Q5287501
cites work: Q4205660
cites work: Q3831482
cites work: Variations and generalizations of Bohr's inequality
cites work: Q3976127
cites work: Q5623936
DOI: 10.1016/J.JMAA.2005.10.046
description: scientific article; zbMATH DE number 5072953