1. Equivalent norms in a banach function space and the subsequence property
- Author
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Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada, Agencia Estatal de Investigación, European Regional Development Fund, Ministerio de Ciencia e Innovación, Ministerio de Economía y Competitividad, Consejo Nacional de Ciencia y Tecnología, México, Calabuig, J. M., Fernández-Unzueta, Maite, Galaz-Fontes, Fernando, Sánchez Pérez, Enrique Alfonso, Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada, Agencia Estatal de Investigación, European Regional Development Fund, Ministerio de Ciencia e Innovación, Ministerio de Economía y Competitividad, Consejo Nacional de Ciencia y Tecnología, México, Calabuig, J. M., Fernández-Unzueta, Maite, Galaz-Fontes, Fernando, and Sánchez Pérez, Enrique Alfonso
- Abstract
[EN] Consider a finite measure space (Omega, Sigma, mu) and a Banach space X(mu) consisting of (equivalence classes of) real measurable functions defined on Omega such that f chi(A) is an element of X(mu) and parallel to f chi(A)parallel to <= parallel to f parallel to, for all f is an element of X(mu), A is an element of Sigma. We prove that if it satisfies the subsequence property, then it is an ideal of measurable functions and has an equivalent norm under which it is a Banach function space. As an application we characterize norms that are equivalent to a Banach function space norm.
- Published
- 2019