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ArticleOriginal scientific text

Title

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

Authors 1, 1

Affiliations

  1. Mathematisches Seminar, Universität Kiel, Ludewig-Meyn-Str. 4, D-24098 Kiel, Germany

Abstract

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 ℓs,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.

Keywords

ENG
entropy numbers, r-nuclear operators, weak type

Bibliography

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Studia Mathematica
1993/107/1
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Pages:
1-14
Main language of publication
English
Received
1992-01-07
Accepted
1993-03-16
Published
1993
Exact and natural sciences