Randomized series and Geometry of Banach spaces

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dc.creatorLee, Han Ju
dc.date2007-06-26
dc.date.accessioned2026-07-07T08:12:24Z
dc.date.available2026-07-07T08:12:24Z
dc.descriptionWe study some properties of the randomized series and their applications to the geometric structure of Banach spaces. For $n\ge 2$ and $1<p<\infty$, it is shown that $\ell_\infty^n$ is representable in a Banach space $X$ if and only if it is representable in the Lebesgue-Bochner $L_p(X)$. New criteria for various convexity properties in Banach spaces are also studied. It is proved that a Banach lattice $E$ is uniformly monotone if and only if its $p$-convexification $E^{(p)}$ is uniformly convex and that a Köthe function space $E$ is upper locally uniformly monotone if and only if its $p$-convexification $E^{(p)}$ is midpoint locally uniformly convex.
dc.identifierhttps://arxiv.org/abs/0706.3740
dc.identifierhttp://arxiv.org/abs/0706.3740
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/132443
dc.subjectFunctional Analysis
dc.subject46B20;46B07;46B09
dc.titleRandomized series and Geometry of Banach spaces
dc.typetext

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