Randomized Series and Geometry of Banach Spaces
نویسنده
چکیده
Abstract. We study some properties of the randomized series and their applications to the geometric structure of Banach spaces. For n ≥ 2 and 1 < p < ∞, it is shown that l ∞ is representable in a Banach space X if and only if it is representable in the Lebesgue-Bochner Lp(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 is uniformly convex and that a Köthe function space E is upper locally uniformly monotone if and only if its p-convexification E is midpoint locally uniformly convex.
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