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Marian Nowak 6FCE?= @K= B ?=O ?LAN HE?*?DAH IF=?AI

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Marian Nowak

Topological dual of non-locally convex Orlicz-Bochner spaces

Comment.Math.Univ.Carolinae 40,3 (1999) 511-529.

Abstract: LetLϕ(X) be an Orlicz-Bochner space defined by an Orlicz functionϕ taking only finite values (not necessarily convex) over aσ-finite atomless measure space. It is proved that the topological dualLϕ(X)∗ ofLϕ(X) can be represented in the form: Lϕ(X)∗ =Lϕ(X)∼n ⊕Lϕ(X)∼s, where Lϕ(X)∼n and Lϕ(X)∼s denote the order continuous dual and the singular dual ofLϕ(X) respectively. The spaces Lϕ(X)∗,Lϕ(X)∼n andLϕ(X)∼s are examined by means of the H. Nakano’s theory of conjugate modulars. (Studia Mathematica 31 (1968), 439–449). The well known results of the duality theory of Orlicz spaces are extended to the vector-valued setting.

Keywords: vector-valued function spaces, Orlicz functions, Orlicz spaces, Orlicz- Bochner spaces, topological dual, order dual, order continuous linear functionals, singular linear functionals, modulars, conjugate modulars

AMS Subject Classification: 46E30, 46E40, 46A20

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