Characterization of weak type by the entropy distribution of r-nuclear operators

Defant, Martin; Junge, Marius

Studia Mathematica, Tome 104 (1993), p. 1-14 / Harvested from The Polish Digital Mathematics Library

Résumé

The dual of a Banach space X is of weak type p if and only if the entropy numbers of an r-nuclear operator with values in a Banach space of weak type q belong to the Lorentz sequence space $ℓ_{s, r}$ with 1/s + 1/p + 1/q = 1 + 1/r (0 < r < 1, 1 ≤ p, q ≤ 2). It is enough to test this for Y = X*. This extends results of Carl, König and Kühn.

Publié le : 1993-01-01

Zbl 0812.47018

EUDML-ID : urn:eudml:doc:216020

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     author = {Martin Defant and Marius Junge},
     title = {Characterization of weak type by the entropy distribution of r-nuclear operators},
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     volume = {104},
     year = {1993},
     pages = {1-14},
     zbl = {0812.47018},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv107i1p1bwm}
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Defant, Martin; Junge, Marius. Characterization of weak type by the entropy distribution of r-nuclear operators. Studia Mathematica, Tome 104 (1993) pp. 1-14. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv107i1p1bwm/

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