Holder Type Inequalities Involving Tracy-Singh Products and Khatri-Rao Products of Hilbert Space Operators

被引：0

作者：

Ploymukda, Arnon ^{[1
]}

Chansangiam, Pattrawut ^{[1
]}

机构：

[1] King Mongkuts Inst Technol Ladkrabang, Dept Math, Fac Sci, Bangkok, Thailand

来源：

COMMUNICATIONS IN MATHEMATICS AND APPLICATIONS | 2019年 / 10卷 / 03期

关键词：

Holder inequality; Tracy-Singh product; Khatri-Rao product; Hilbert space operator; CONCAVITY; MAPS; SUMS;

D O I：

10.26713/cma.v10i3.1227

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper generalizes the famous Holder type inequalities for positive real numbers to positive operators on an arbitrary complex Hilbert space. We use appropriate integral representations of certain operator-monotone functions to deduce the concavity and convexity of certain maps involving Tracy-Singh products of operators. These results lead to Holder type inequalities for operators concerning Tracy-Singh products, Khatri-Rao products, Tracy-Singh sums, and Khatri-Rao sums. In particular, we obtain Cauchy-Schwarz type inequalities for operators involving Tracy-Singh products and Khatri-Rao products.

引用

页码：531 / 540

页数：10

共 20 条

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Ploymukda, Arnon
Chansangiam, Pattrawut
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[J]. MALAYSIAN JOURNAL OF FUNDAMENTAL AND APPLIED SCIENCES, 2018, 14 (04): : 382 - 386
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