Strictly singular inclusions into L1+L∞
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2008
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Springer
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Abstract
It is given a complete characterization of the strict singularity and the disjoint strict singularity of the inclusions E → L1 + L∞ for the class of rearrangement invariant function spaces E on the [0,∞) interval. Their relationship is also analyzed. Suitable criteria
are given involving the scale of order continuous weak L p-spaces for 1 < p < ∞.
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Francisco L. Hernández and Víctor M. Sánchez were partially supported by the Spanish Ministry of Education, grant MTM2005-00082 and Complutense-Santander grant PR27/05-14045.
Evgeny M. Semenov was partially supported by RFBR (Russia), grant 05-01-00629, by Universities of Russia grant 04.01.051 and by a Spanish Ministry of Education grant SAB2002.