Spaces of cone absolutely summing maps are generalizations of Bochner spaces L p(μ, Y), where (Ω, Σ, μ) is some measure space, 1 ≤ p ≤ ∞ and Y is a Banach space. The Hiai-Umegaki space of integrably bounded functions F: Ω → cbf(X), where the latter denotes the set of all convex bounded closed subsets of a separable Banach space X, is a set-valued analogue of L 1(μ, X). The aim of this work is to introduce set-valued cone absolutely summing maps as a generalization of , and to derive necessary and sufficient conditions for a set-valued map to be such a set-valued cone absolutely summing map. We also describe these set-valued cone absolutely summing maps as those that map order-Pettis integrable functions to integrably bounded set-valued functions.
@article{bwmeta1.element.doi-10_2478_s11533-009-0059-7,
author = {Coenraad Labuschagne and Valeria Marraffa},
title = {On set-valued cone absolutely summing maps},
journal = {Open Mathematics},
volume = {8},
year = {2010},
pages = {148-157},
zbl = {1185.28019},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-009-0059-7}
}
Coenraad Labuschagne; Valeria Marraffa. On set-valued cone absolutely summing maps. Open Mathematics, Tome 8 (2010) pp. 148-157. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-009-0059-7/
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