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Open AccessArticle

Banach Lattice Structures and Concavifications in Banach Spaces

1
Departamento de Matemática Aplicada, Universitat Politècnica de València, Campus de Alcoy, 03801 Alicante, Spain
2
Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain
3
Faculty of Administración y Dirección de Empresas (ADE), Universidad Católica de Valencia, 46001 Valencia, Spain
*
Author to whom correspondence should be addressed.
All the authors contributed equally to this work.
Mathematics 2020, 8(1), 127; https://doi.org/10.3390/math8010127
Received: 15 December 2019 / Revised: 8 January 2020 / Accepted: 10 January 2020 / Published: 14 January 2020
(This article belongs to the Section Mathematics and Computer Science)
Let ( Ω , Σ , μ ) be a finite measure space and consider a Banach function space Y ( μ ) . We say that a Banach space E is representable by Y ( μ ) if there is a continuous bijection I : Y ( μ ) E . In this case, it is possible to define an order and, consequently, a lattice structure for E in such a way that we can identify it as a Banach function space, at least regarding some local properties. General and concrete applications are shown, including the study of the notion of the pth power of a Banach space, the characterization of spaces of operators that are isomorphic to Banach lattices of multiplication operators, and the representation of certain spaces of homogeneous polynomials on Banach spaces as operators acting in function spaces. View Full-Text
Keywords: Banach function space; concavification; local theory; Banach space; strongly p-integral operator; pth power Banach function space; concavification; local theory; Banach space; strongly p-integral operator; pth power
MDPI and ACS Style

Agud, L.; Calabuig, J.M.; Juan, M.A.; Sánchez Pérez, E.A. Banach Lattice Structures and Concavifications in Banach Spaces. Mathematics 2020, 8, 127.

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