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
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