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Some convexity properties of Musielak-Orlicz spaces of Bochner type. (English) Zbl 0609.46015

It is shown here that if a Banach space X and Musielak-Orlicz space \(L_{\phi}\) are both locally uniformly rotund or uniformly rotund in every direction then the space \(L_{\phi}(X)\) of Bochner type has the same properties. Moreover criteria for these properties have been given for a subspace of finite elements \(E_{\phi}(X)\).

MSC:

46E40 Spaces of vector- and operator-valued functions
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
46B25 Classical Banach spaces in the general theory
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