Submultiplicativity vs subadditivity for unitarily invariant norms

Fumio Hiai; Xingzhi Zhan

doi:10.1016/j.laa.2003.08.006

Submultiplicativity vs subadditivity for unitarily invariant norms

Fumio Hiai^*
, Xingzhi Zhan

^*此作品的通讯作者

数学科学学院

Tohoku University

科研成果: 期刊稿件 › 文章 › 同行评审

4 引用（Scopus）

摘要

Let A, B be nonzero positive semidefinite matrices. We prove that ∥AB∥/∥A∥ ∥B∥ ≤ ∥A + B∥/∥A∥+∥B∥,∥A ο B∥/∥A∥ ∥B∥ ≤ ∥A + B∥/∥A∥ + ∥B∥ for any unitarily invariant norm with ∥diag(1, 0,..., 0)∥ ≥ 1. Some related inequalities are derived.

源语言	英语
页（从-至）	155-164
页数	10
期刊	Linear Algebra and Its Applications
卷	377
期	1-3
DOI	https://doi.org/10.1016/j.laa.2003.08.006
出版状态	已出版 - 15 1月 2004

访问文件

10.1016/j.laa.2003.08.006

其它文件与链接

链接到 Scopus 的出版物

引用此

@article{80358fc9b68c4bd884776a683e998abf,

title = "Submultiplicativity vs subadditivity for unitarily invariant norms",

abstract = "Let A, B be nonzero positive semidefinite matrices. We prove that ∥AB∥/∥A∥ ∥B∥ ≤ ∥A + B∥/∥A∥+∥B∥,∥A ο B∥/∥A∥ ∥B∥ ≤ ∥A + B∥/∥A∥ + ∥B∥ for any unitarily invariant norm with ∥diag(1, 0,..., 0)∥ ≥ 1. Some related inequalities are derived.",

keywords = "Hadamard product, Majorization, Matrix Young inequality, Positive semidefinite matrix, Subadditivity, Submultiplicativity, Unitarily invariant norm",

author = "Fumio Hiai and Xingzhi Zhan",

year = "2004",

month = jan,

day = "15",

doi = "10.1016/j.laa.2003.08.006",

language = "英语",

volume = "377",

pages = "155--164",

journal = "Linear Algebra and Its Applications",

issn = "0024-3795",

publisher = "Elsevier Inc.",

number = "1-3",

}

TY - JOUR

T1 - Submultiplicativity vs subadditivity for unitarily invariant norms

AU - Hiai, Fumio

AU - Zhan, Xingzhi

PY - 2004/1/15

Y1 - 2004/1/15

N2 - Let A, B be nonzero positive semidefinite matrices. We prove that ∥AB∥/∥A∥ ∥B∥ ≤ ∥A + B∥/∥A∥+∥B∥,∥A ο B∥/∥A∥ ∥B∥ ≤ ∥A + B∥/∥A∥ + ∥B∥ for any unitarily invariant norm with ∥diag(1, 0,..., 0)∥ ≥ 1. Some related inequalities are derived.

AB - Let A, B be nonzero positive semidefinite matrices. We prove that ∥AB∥/∥A∥ ∥B∥ ≤ ∥A + B∥/∥A∥+∥B∥,∥A ο B∥/∥A∥ ∥B∥ ≤ ∥A + B∥/∥A∥ + ∥B∥ for any unitarily invariant norm with ∥diag(1, 0,..., 0)∥ ≥ 1. Some related inequalities are derived.

KW - Hadamard product

KW - Majorization

KW - Matrix Young inequality

KW - Positive semidefinite matrix

KW - Subadditivity

KW - Submultiplicativity

KW - Unitarily invariant norm

UR - https://www.scopus.com/pages/publications/0242303536

U2 - 10.1016/j.laa.2003.08.006

DO - 10.1016/j.laa.2003.08.006

M3 - 文章

AN - SCOPUS:0242303536

SN - 0024-3795

VL - 377

SP - 155

EP - 164

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 1-3

ER -

Submultiplicativity vs subadditivity for unitarily invariant norms

摘要

访问文件

其它文件与链接

指纹

引用此