Published January 8, 2021 | Version v1
Publication

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

Description

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.

Abstract

Ministerio de Economía y Competitividad MTM2012-36732-C03-03

Abstract

Junta de Andalucía FQM-262

Abstract

Junta de Andalucía FQM-7276

Additional details

Created:
December 4, 2022
Modified:
November 30, 2023