Parametric extensions of Shannon inequality and its reverse one in Hilbert space operators.
type: Item
instance of: scholarly article
title: Parametric extensions of Shannon inequality and its reverse one in Hilbert space operators.
zbMATH Open document ID: 1057.47022
author: Takayuki Furuta
published in: Linear Algebra and its Applications
publication date: 2004-05-27T00:00:00Z
review text: The Shannon inequality asserts that if \(\{a_1,\dots, a_n\}\) and \(\{b_1,\dots, b_n\}\) are two probability vectors, then \(\sum^n_{j=1} a_j\log{b_j\over a_j}\leq 0\). The authors give parametric extensions of the Shannon inequality and its reverse for Hilbert space operators.
reviewed by: Omar Hirzallah
Mathematics Subject Classification ID: 47A63
Mathematics Subject Classification ID: 94A17
Mathematics Subject Classification ID: 60E15
Mathematics Subject Classification ID: 26D15
zbMATH DE Number: 2069728
zbMATH Keywords: Shannon inequality
zbMATH Keywords: reverse type Shannon inequality
zbMATH Keywords: operator concave function
MaRDI profile type: Publication
full work available at URL: j.laa.2003.11.017
OpenAlex ID: W2029533580
cites work: Q4265267
cites work: Q3477514
cites work: Q3471077
cites work: An operator inequality
cites work: Jensen's inequality for operators and Loewner's theorem
cites work: Some results on matrix monotone functions
cites work: On Information and Sufficiency
cites work: A note on the entropy for operator algebras
cites work: A Mathematical Theory of Communication
cites work: JENSEN'S OPERATOR INEQUALITY
DOI: 10.1016/J.LAA.2003.11.017
description: scientific article; zbMATH DE number 2069728