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 Equivalent norms in a Banach function space and the subsequence property J. Korean Math. Soc. 2019 Vol. 56, No. 5, 1387-1401 https://doi.org/10.4134/JKMS.j180682Published online September 1, 2019 Jose M. Calabuig, Maite Fern\'andez-Unzueta, Fernando Galaz-Fontes, Enrique A. S\'{a}nchez-P\'{e}rez Universitat Polit\{e}cnica de Val\encia; Centro de Investigaci\'on en Matem\'aticas, A.C.; Centro de Investigaci\'on en Matem\'aticas, A.C.; Universitat Polit\{e}cnica de Val\encia Abstract : Consider a finite measure space $(\Ome,\Sig,\mu)$ and a Banach space $X(\mu)$ consisting of (equivalence classes of) real measurable functions defined on $\Ome$ such that $f\chi_A \in X(\mu)$ and $\|f\chi_A \| \leq \|f\|, \ \pt f \in X(\mu), \ A \in \Sig$. 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. Keywords : measure space, space of measurable functions, order, Banach function space MSC numbers : 46E30, 46B42 Downloads: Full-text PDF   Full-text HTML