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Pré-Publication, Document De Travail Année : 2021

A duality operators/Banach spaces

Résumé

Given a set $B$ of operators between subspaces of $L_p$ spaces, we characterize the operators between subspaces of $L_p$ spaces that remain bounded on the $X$-valued $L_p$ space for every Banach space on which elements of the original class $B$ are bounded. This is a form of the bipolar theorem for a duality between the class of Banach spaces and the class of operators between subspaces of $L_p$ spaces, essentially introduced by Pisier. The methods we introduce allow us to recover also the other direction --characterizing the bipolar of a set of Banach spaces--, which had been obtained by Hernandez in 1983.

Dates et versions

hal-03264856 , version 1 (18-06-2021)

Identifiants

Citer

Mikael de La Salle. A duality operators/Banach spaces. 2021. ⟨hal-03264856⟩
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