Young's (in)equality for compact operators

Authors
Larotonda, Gabriel Andrés
Publication Year
2016
Language
English
Format
article
Status
Published version
Description
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 λk(|ab∗ |) ≤ λk 1 p |a| p + 1 q |b| q for all k. Later, this result was extended for the singular values of a pair of compact operators acting on a Hilbert space by J. Erlijman, D. 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 .
Fil: Larotonda, Gabriel Andrés. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderon; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina
Subject
YOUNG INEQUALITY
COMPACT OPERATOR
SINGULAR VALUE
SPECTRUM
Matemática Pura
Matemáticas
CIENCIAS NATURALES Y EXACTAS
Access level
Restricted access
License
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repository
CONICET Digital (CONICET)
Institution
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identifier
oai:ri.conicet.gov.ar:11336/18948