Banach Lattice Structures and Concavifications in Banach Spaces

Lucia Agud, Jose Manuel Calabuig, Maria Aranzazu Juan and Enrique A. Sánchez Pérez
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Lucia Agud: Departamento de Matemática Aplicada, Universitat Politècnica de València, Campus de Alcoy, 03801 Alicante, Spain
Jose Manuel Calabuig: Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain
Maria Aranzazu Juan: Faculty of Administración y Dirección de Empresas (ADE), Universidad Católica de Valencia, 46001 Valencia, Spain
Enrique A. Sánchez Pérez: Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain

Mathematics, 2020, vol. 8, issue 1, 1-20

Abstract: 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 p th 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.

Keywords: Banach function space; concavification; local theory; Banach space; strongly p -integral operator; p th power (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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