Geodesic
An Application of Kadets–Pełczyński Sets to Narrow Operators
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 9 (2013) no. 1, pp. 102-107 
I. V. Krasikova; M. M. Popov. An Application of Kadets–Pełczyński Sets to Narrow Operators. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 9 (2013) no. 1, pp. 102-107. http://geodesic.mathdoc.fr/item/JMAG_2013_9_1_a6/
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Voir la notice de l'article provenant de la source Math-Net.Ru

A known analogue of the Pitt compactness theorem for function spaces asserts that if $1 \leq p < 2$ and $p < r < \infty$, then every operator $T:L_p \to L_r$ is narrow. Using a technique developed by M. I. Kadets and A. Pełczyński, we prove a similar result. More precisely, if $1 \leq p \leq 2$ and $F$ is a Köthe–Banach space on $[0,1]$ with an absolutely continuous norm containing no isomorph of $L_p$ such that $F \subset L_p$, then every regular operator $T: L_p \to F$ is narrow.

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