Young's (in)equality for compact operators

Gabriel Larotonda

Studia Mathematica, Tome 233 (2016), p. 169-181 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $λ_{k} (| a b * |) \leq λ_{k} {(1 / p | a |}^{p} + 1 / {q | b |}^{q})$ 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 ${| a |}^{p} = {| b |}^{q}$ .

Publié le : 2016-01-01

Zbl 06586874

EUDML-ID : urn:eudml:doc:285843

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     title = {Young's (in)equality for compact operators},
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     volume = {233},
     year = {2016},
     pages = {169-181},
     zbl = {06586874},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm8427-5-2016}
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Gabriel Larotonda. Young's (in)equality for compact operators. Studia Mathematica, Tome 233 (2016) pp. 169-181. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm8427-5-2016/