Disjoint strict singularity of inclusions between rearrangement invariant spaces



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Hernández, Francisco L. and Sánchez de los Reyes, Víctor Manuel and Semenov, Evgeny M. (2001) Disjoint strict singularity of inclusions between rearrangement invariant spaces. Studia Mathematica, 144 (3). pp. 209-226. ISSN 0039-3223

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It is studied when inclusions between rearrangement invariant function spaces on the interval [0, infinity) are disjointly strictly singular operators. In particular suitable criteria, in terms of the fundamental function, for the inclusions L 1 ∩L ∞ ↪E and E↪L 1 +L ∞ to be disjointly strictly singular are shown. Applications to the classes of Lorentz and Marcinkiewicz spaces are given.

Item Type:Article
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The authors wish to thank the referee for his suggestions and detailed remarks.

Uncontrolled Keywords:Rearrangement invariant function spaces; Inclusion operator; Strictly singular; Weakly compact; Lorentz and Marcinkiewicz spaces
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:19909
Deposited On:12 Feb 2013 16:35
Last Modified:27 Jun 2018 07:34

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