Matrix inequalities related to Hölder inequality
type: Item
instance of: scholarly article
title: Matrix inequalities related to Hölder inequality
zbMATH Open document ID: 1270.15012
author: Hussien Albadawi
published in: Banach Journal of Mathematical Analysis
publication date: 2013-03-20T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.bjma/1363784229
review text: The main results of this paper are Hölder-type matrix inequalities for sums and products of matrices that generalize a Hölder-type matrix inequality proved by \textit{T. Ando} and \textit{F. Hiai} [Math. Inequal. Appl. 1, No. 1, 1--30 (1998; Zbl 0897.15008)]. One of these results is the following theorem: Let \(2 \leqslant p,q \leqslant \infty\) und \(r > 1\) with \(1/p+1/q=1-1/r\). Then for any \({A_i},{B_i} \in {M_n}({\mathbb C})\) and \({\alpha _i} \in [0,1]\) \((i = 1,2,\dots,m)\) with \(\sum_{i = 1}^m {{\alpha _i} = 1}\), we have \(\left| \sum_{i = 1}^m \alpha _i^{1/r} B_i A_i\right| \leqslant \left(\sum_{i = 1}^m \left| A_i \right|^p \right)^{1/p}\) whenever \(\sum_{i = 1}^m \left| B_i^* \right|^q\).
reviewed by: Mihail Voicu
Mathematics Subject Classification ID: 15A45
Mathematics Subject Classification ID: 47A30
Mathematics Subject Classification ID: 15A60
Mathematics Subject Classification ID: 15B48
zbMATH DE Number: 6147465
zbMATH Keywords: Hölder-type matrix inequality
MaRDI profile type: Publication
OpenAlex ID: W1969645104
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DOI: 10.15352/BJMA/1363784229
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description: scientific article; zbMATH DE number 6147465