2015/11/07 by O. Delgado, Delgado, O., Enrique A. Sánchez‐Pérez +2
Mathematics · #46B42 #46E30 #46G10 #47B38 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:46B42 #msc:46E30 #msc:46G10 #msc:47B38
paper · pdf · doi:10.48550/arxiv.1511.02337
arxiv created 2015/11/07 · openalex publication_date 2015/11/07 · arxiv updated 2015/11/10 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.