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arXiv · 1810.05714

Equivalent Norms in a Banach Function Space and the Subsequence Property

Jose M. Calabuig·Maite Fernández Unzueta·Fernando Galaz-Fontes·Enrique A. Sánchez Pérez
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Abstract

Given a finite measure space $(Ω,Σ,μ)$, we show that any Banach space $X(μ)$ consisting of (equivalence classes of) real measurable functions defined on $Ω$ such that $f χ_A \in X(μ) $ and $ \|f χ_A \| \leq \|f\|, \, f \in X(μ), \ A \in Σ$, and having the subsequence property, is in fact 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.

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Jose M. Calabuig, Maite Fernández Unzueta, Fernando Galaz-Fontes, Enrique A. Sánchez Pérez. 2018-10-12. Equivalent Norms in a Banach Function Space and the Subsequence Property. https://arxiv.org/abs/1810.05714

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