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arXiv · 1511.02337

Optimal domain of $q$-concave operators and vector measure representation of $q$-concave Banach lattices

O. Delgado·E. A. Sanchez Perez
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Abstract

Given a Banach space valued $q$-concave linear operator $T$ defined on a $σ$-order continuous quasi-Banach function space, we provide a description of the optimal domain of $T$ preserving $q$-concavity, that is, the largest $σ$-order continuous quasi-Banach function space to which $T$ can be extended as a $q$-concave operator. We show in this way the existence of maximal extensions for $q$-concave operators. As an application, we show a representation theorem for $q$-concave Banach lattices through spaces of integrable functions with respect to a vector measure. This result culminates a series of representation theorems for Banach lattices using vector measures that have been obtained in the last twenty years.

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O. Delgado, E. A. Sanchez Perez. 2015-11-07. Optimal domain of $q$-concave operators and vector measure representation of $q$-concave Banach lattices. https://arxiv.org/abs/1511.02337

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