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

Kamińska, A.

Rend. Circ. Mat. Palermo, II. Ser. Suppl. 10, 63-73 (1985).

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

Keywords:

Musielak-Orlicz spaces of Bochner type; locally uniformly rotund; uniformly rotund in every direction