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Some class of uniformly non-square Orlicz-Bochner spaces. (English) Zbl 0579.46022

It is proved that if X is a uniformly convex normed space, \(\mu\) is a non-negative and \(\sigma\)-finite measure and \(\Phi\) is a uniformly convex Orlicz function satisfying suitable condition \(\Delta_ 2\), then the Orlicz-Bochner space \(L^{\Phi}(\mu,X)\) is uniformly non-square. Necessity of uniform non-squareness of X and of suitable condition \(\Delta_ 2\) for \(\Phi\) is also proved. Finally, some question is given.

MSC:

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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