Universidad Complutense de Madrid
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Strictly singular embeddings in L 1 +L ∞

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Sánchez de los Reyes, Víctor Manuel and Semenov, Evgeny M. and Hernández, Francisco L. (2005) Strictly singular embeddings in L 1 +L ∞. Doklady Mathematics, 71 (3). pp. 388-390. ISSN 1064-5624


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Abstract

The paper deals with the strict singularity and the disjoint strict singularity of the canonical embedding
between couples of rearrangement invariant spaces E and F. Let E c F. This embedding is called strictly singular (disjointly strictly singular) if for any infinite-dimensional subspace (any infinite-dimensional subspace generated by a sequence of disjoint functions) B of E the norms of E and F are non-equivalent on B. Denote by Lp,1 (1 < p < 1) the space of all measurable functions x(t) on (0,1) such that kxkLp,1 = sup s>0 s1/p−1 Z s 0 x(t) dt <1.


Item Type:Article
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:19888
Deposited On:11 Feb 2013 15:33
Last Modified:08 Nov 2013 18:13

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