Young's (in)equality for compact operators
Studia Mathematica, Tome 233 (2016) no. 2, p. 169.

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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 ( | a b * | ) ≤ 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 .
Classification : 47A30, 47A63, 15A42, 15A45
Mots-clés : compact operator, Young inequality, operator ideal, singular value equality 
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Gabriel Larotonda. Young's (in)equality for compact operators. Studia Mathematica, Tome 233 (2016) no. 2, p. 169. https://geodesic-test.mathdoc.fr/item/STUMA_2016__233_2_285843/