CONICET | Buscador de Institutos y Recursos Humanos

If $a,b$ are $nimes n$ matrices, Ando proved that Young´s inequality is valid for their singular values: if $p>1$ and $1/p+1/q=1$, then$$lambda_k(|ab^*|)le lambda_kleft( rac1p |a|^p+rac 1q |b|^q ight) , extit{ for all }k.$$Later, this result was extended for the singular values of a pair of compact operators acting on a Hilbert space by Erlijman, Farenick and Zeng. In this paper we prove that if $a,b$ are compact operators, then equality holds in Young´s inequality if and only if $|a|^p=|b|^q$.