A new proof of an inequality of Bohr for Hilbert space operators
type: Item
instance of: scholarly article
title: A new proof of an inequality of Bohr for Hilbert space operators
zbMATH Open document ID: 1162.47016
author: S. Abramovich
author: J. Barić
author: J. Pečarić
published in: Linear Algebra and its Applications
publication date: 2009-02-10T00:00:00Z
review text: The authors give a simple proof of Bohr's inequality for Hilbert space operators, i.e., \[ |A-B|^{2}+|(1-p)A-B|^{2}\leq p|A|^{2}+q|B|^{2} \] for \(\frac{1}{p}+\frac{1}{q}=1\) and \(A,B\in B(H)\). In the proof, which simplifies the one in [\textit{W.--S.\thinspace Cheung} and \textit{J.\,Pečarić}, J.~Math.\ Anal.\ Appl.\ 323, 403--412 (2006; Zbl 1108.26018)], the authors point out that the equality \[ p|A|^{2}+q|B|^{2}=|A-B|^{2}+\frac{1}{p-1}|(p-1)A+B|^{2} \] is important.
reviewed by: Takeaki Yamazaki
Mathematics Subject Classification ID: 47A63
Mathematics Subject Classification ID: 26D15
Mathematics Subject Classification ID: 46C05
zbMATH DE Number: 5505639
zbMATH Keywords: Bohr's inequality
MaRDI profile type: Publication
full work available at URL: j.laa.2008.09.041
OpenAlex ID: W2076579034
cites work: On Bohr’s Inequalities
cites work: Bohr's inequalities for Hilbert space operators
cites work: Non-commutative operator Bohr inequality
cites work: Q5287501
cites work: Q4205660
cites work: Variations and generalizations of Bohr's inequality
cites work: Q5623936
DOI: 10.1016/J.LAA.2008.09.041
description: scientific article; zbMATH DE number 5505639