## 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
Full Text: