A factorization theorem in Banach lattices and its application to Lorentz spaces

Reisner, Sholomo

Annales de l'Institut Fourier, Tome 31 (1981) no. 1, pp. 239-255.

On caractérise la $p$-convexité et la $q$-concavité d’un treillis de Banach $L$ à l’aide de la factorisation des opérateurs de multiplication de $L_q$ dans $L_p$ à travers l’espace $L$. Cette caractérisation est utilisée pour calculer le type de concavité des espace de Lorentz.

$p$-convexity and $q$-concavity of a Banach lattice $L$ are characterized by factorization of multiplication operators from $L_q$ into $L_p$ through $L$. This characterization is applied to calculate the concavity type of Lorentz spaces.

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