Journal of Operator Theory

Volume 77, Issue 2, Spring 2017 pp. 261-286.

Power concave operators and representation of $p$-convex and $q$-concave Banach lattices

Authors: Olvido Delgado (1) and Enrique A. Sanchez Perez (2)
Author institution: (1) Departamento de Matematica Aplicada I, E. T. S. de Ingenieria de Edificacion, Universidad de Sevilla, Sevilla, 41012, Spain
(2) Instituto Universitario de Matematica Pura y Aplicada, Universitat Politecnica de Valencia, Valencia, 46022, Spain

Summary: As a consequence of the analysis of the class of $(p,q)$-power concave operators, we prove a general representation theorem for $p$-convex and $q$-concave Banach lattices as spaces of integrable functions with respect to vector measures. This result culminates a series of representation theorems for Banach lattices using vector measures that have been obtained in the last twenty years.

DOI: http://dx.doi.org/10.7900/jot.2016feb21.2137
Keywords: Banach lattices, $q$-concave operators, quasi-Banach function spaces, vector measures, $\delta$-ring

Contents Full-Text PDF