This is an announcement for the paper “Equivalent Norms in a Banach Function Space and the Subsequence Property” by Jose M. Calabuighttps://arxiv.org/search/math?searchtype=author&query=Calabuig%2C+J+M, Maite Fernández Unzuetahttps://arxiv.org/search/math?searchtype=author&query=Unzueta%2C+M+F, Fernando Galaz-Fonteshttps://arxiv.org/search/math?searchtype=author&query=Galaz-Fontes%2C+F, Enrique A. Sánchez Pérezhttps://arxiv.org/search/math?searchtype=author&query=P%C3%A9rez%2C+E+A+S.
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.
The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1810.05714