Generalized noncommutative Hardy and Hardy-Hilbert type inequalities

Frank Hansen; Kristina Krulić; Josip Pečarić; Lars Erik Persson

doi:10.1142/S0129167X10006501

Generalized noncommutative Hardy and Hardy-Hilbert type inequalities

Frank Hansen, Kristina Krulić, Josip Pečarić, Lars Erik Persson

Division of Developmental Research in Education Programs

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

We extend and unify several Hardy type inequalities to functions whose values are positive semi-definite operators. In particular, our methods lead to the operator versions of Hardy-Hilbert's and Godunova's inequalities. While classical Hardy type inequalities hold for parameter values p > 1, it is typical that the operator versions hold only for 1 < p ≤ 2, even for functions with values in 2 × 2 matrices.

Original language	English
Pages (from-to)	1283-1295
Number of pages	13
Journal	International Journal of Mathematics
Volume	21
Issue number	10
DOIs	https://doi.org/10.1142/S0129167X10006501
Publication status	Published - 2010 Oct 1

Keywords

Godunova's inequality
Hardy's inequality
Hardy-Hilbert's inequality
Inequalities
operator convex functions
positive operator
weights

ASJC Scopus subject areas

Mathematics(all)

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10.1142/S0129167X10006501

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abstract = "We extend and unify several Hardy type inequalities to functions whose values are positive semi-definite operators. In particular, our methods lead to the operator versions of Hardy-Hilbert's and Godunova's inequalities. While classical Hardy type inequalities hold for parameter values p > 1, it is typical that the operator versions hold only for 1 < p ≤ 2, even for functions with values in 2 × 2 matrices.",

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language = "English",

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AU - Krulić, Kristina

AU - Pečarić, Josip

AU - Persson, Lars Erik

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Y1 - 2010/10/1

N2 - We extend and unify several Hardy type inequalities to functions whose values are positive semi-definite operators. In particular, our methods lead to the operator versions of Hardy-Hilbert's and Godunova's inequalities. While classical Hardy type inequalities hold for parameter values p > 1, it is typical that the operator versions hold only for 1 < p ≤ 2, even for functions with values in 2 × 2 matrices.

AB - We extend and unify several Hardy type inequalities to functions whose values are positive semi-definite operators. In particular, our methods lead to the operator versions of Hardy-Hilbert's and Godunova's inequalities. While classical Hardy type inequalities hold for parameter values p > 1, it is typical that the operator versions hold only for 1 < p ≤ 2, even for functions with values in 2 × 2 matrices.

KW - Godunova's inequality

KW - Hardy's inequality

KW - Hardy-Hilbert's inequality

KW - Inequalities

KW - operator convex functions

KW - positive operator

KW - weights

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Generalized noncommutative Hardy and Hardy-Hilbert type inequalities

Abstract

Keywords

ASJC Scopus subject areas

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