Weak majorization, doubly substochastic maps, and some related inequalities in Euclidean Jordan algebras

Juyoung Jeong; Yoon Mo Jung; Yongdo Lim

doi:10.1016/j.laa.2020.03.028

Weak majorization, doubly substochastic maps, and some related inequalities in Euclidean Jordan algebras

Juyoung Jeong, Yoon Mo Jung, Yongdo Lim

Department of Mathematics

Sungkyunkwan University

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

5 Scopus citations

Abstract

In this paper, we extend the notion of weak majorization and doubly substochastic maps, and the Hardy-Littlewood-Pólya theorem on majorization to Euclidean Jordan algebras. We also provide a characterization of doubly substochastic maps on Euclidean Jordan algebras in terms of Jordan algebra automorphisms and quadratic representations. In conjunction with that, various weak majorization inequalities of Aujla-Silva are generalized to Euclidean Jordan algebras.

Original language	English
Pages (from-to)	133-154
Number of pages	22
Journal	Linear Algebra and Its Applications
Volume	597
DOIs	https://doi.org/10.1016/j.laa.2020.03.028
State	Published - 15 Jul 2020

Keywords

Doubly substochastic map
Eigenvalue inequality
Euclidean Jordan algebra
Weak majorization

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10.1016/j.laa.2020.03.028

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title = "Weak majorization, doubly substochastic maps, and some related inequalities in Euclidean Jordan algebras",

abstract = "In this paper, we extend the notion of weak majorization and doubly substochastic maps, and the Hardy-Littlewood-P{\'o}lya theorem on majorization to Euclidean Jordan algebras. We also provide a characterization of doubly substochastic maps on Euclidean Jordan algebras in terms of Jordan algebra automorphisms and quadratic representations. In conjunction with that, various weak majorization inequalities of Aujla-Silva are generalized to Euclidean Jordan algebras.",

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AU - Jung, Yoon Mo

AU - Lim, Yongdo

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Y1 - 2020/7/15

N2 - In this paper, we extend the notion of weak majorization and doubly substochastic maps, and the Hardy-Littlewood-Pólya theorem on majorization to Euclidean Jordan algebras. We also provide a characterization of doubly substochastic maps on Euclidean Jordan algebras in terms of Jordan algebra automorphisms and quadratic representations. In conjunction with that, various weak majorization inequalities of Aujla-Silva are generalized to Euclidean Jordan algebras.

AB - In this paper, we extend the notion of weak majorization and doubly substochastic maps, and the Hardy-Littlewood-Pólya theorem on majorization to Euclidean Jordan algebras. We also provide a characterization of doubly substochastic maps on Euclidean Jordan algebras in terms of Jordan algebra automorphisms and quadratic representations. In conjunction with that, various weak majorization inequalities of Aujla-Silva are generalized to Euclidean Jordan algebras.

KW - Doubly substochastic map

KW - Eigenvalue inequality

KW - Euclidean Jordan algebra

KW - Weak majorization

UR - https://www.scopus.com/pages/publications/85082123075

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DO - 10.1016/j.laa.2020.03.028

M3 - Article

AN - SCOPUS:85082123075

SN - 0024-3795

VL - 597

SP - 133

EP - 154

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

ER -

Weak majorization, doubly substochastic maps, and some related inequalities in Euclidean Jordan algebras

Abstract

Keywords

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