Young's (in)equality for compact operators

Gabriel Larotonda. "Young's (in)equality for compact operators." Studia Mathematica 233.2 (2016): 169-181. <http://eudml.org/doc/285843>.

@article{GabrielLarotonda2016,
abstract = {If a,b are n × n matrices, T. Ando proved that Young’s inequality is valid for their singular values: if p > 1 and 1/p + 1/q = 1, then $λ_\{k\}(|ab*|) ≤ λ_\{k\}(1/p |a|^\{p\} + 1/q |b|^\{q\})$ for all k. Later, this result was extended to the singular values of a pair of compact operators acting on a Hilbert space by J. Erlijman, D. R. Farenick and R. Zeng. In this paper we prove that if a,b are compact operators, then equality holds in Young’s inequality if and only if $|a|^\{p\} = |b|^\{q\}$.},
author = {Gabriel Larotonda},
journal = {Studia Mathematica},
keywords = {compact operator; Young inequality; operator ideal; singular value equality},
language = {eng},
number = {2},
pages = {169-181},
title = {Young's (in)equality for compact operators},
url = {http://eudml.org/doc/285843},
volume = {233},
year = {2016},
}

TY - JOUR
AU - Gabriel Larotonda
TI - Young's (in)equality for compact operators
JO - Studia Mathematica
PY - 2016
VL - 233
IS - 2
SP - 169
EP - 181
AB - If a,b are n × n matrices, T. Ando proved that Young’s inequality is valid for their singular values: if p > 1 and 1/p + 1/q = 1, then $λ_{k}(|ab*|) ≤ λ_{k}(1/p |a|^{p} + 1/q |b|^{q})$ for all k. Later, this result was extended to the singular values of a pair of compact operators acting on a Hilbert space by J. Erlijman, D. R. Farenick and R. Zeng. In this paper we prove that if a,b are compact operators, then equality holds in Young’s inequality if and only if $|a|^{p} = |b|^{q}$.
LA - eng
KW - compact operator; Young inequality; operator ideal; singular value equality
UR - http://eudml.org/doc/285843
ER -