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$% H. Hudzik, On some convexity properties of Orlicz spaces of vector valued functions, Rev. Mat. Univ. Complut. Madrid 2 (1989), supplementary, 137–144.%$

On Some Convexity Properties of Orlicz Spaces of Vector Valued Functions

Henryk HUDZIK
Institute of Mathematics
A. Mickiewski University
and Mathematical Institute of
the Polish Academy of Sciences
(Poznan Branch)
Poznan -- Poland

ABSTRACT

A “stability” theorem that is a generalization of Th. 6 in Dowing and Turett (1983) for the modulus of convexity of Banach spaces is given. Necessary and sufficient conditions for @LP(a)> 0 , where a (- (0,2] , in Orlicz spaces LP(,X) of vector valued functions are given. The convexity coefficient P e0(L (m,X)) is computed for these spaces. The equality P e0(L (,X))= e0(X) for Orlicz-Bochner spaces generated by uniformly convex Orlicz functions satisfying the D2 -condition is showed.

1980 Mathematics Subject Classification (1985 revision): 46E30.