Young's (in)equality for compact operators

• Autorzy: Gabriel Larotonda
• Języki publikacji: EN

Abstrakty

EN

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 $|a|^{p} = |b|^{q}$.

Kategorie tematyczne

• 47A30: Norms (inequalities, more than one norm, etc.)
• 15A42: Inequalities involving eigenvalues and eigenvectors
• 47A63: Operator inequalities
• 15A45: Miscellaneous inequalities involving matrices

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2016
• Tom: 233
• Numer: 2
• Strony: 169-181

Daty

wydano

2016

Twórcy

autor

Gabriel Larotonda

• Instituto de Ciencias, Universidad Nacional de General Sarmiento, J. M. Gutierrez 1150, (B1613GSX) Los Polvorines, Buenos Aires, Argentina

Identyfikatory

DOI

10.4064/sm8427-5-2016