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Uniform convexity of Köthe-Bochner function spaces. (English) Zbl 1164.46329

Summary: Of concern are the Köthe-Bochner function spaces \(E(X)\), where \(X\) is a real Banach space. We show that \(E(X)\) is uniformly convex if and only if both spaces \(E\) and \(X\) are uniformly convex.

MSC:

46E40 Spaces of vector- and operator-valued functions
46B20 Geometry and structure of normed linear spaces
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