Displaying similar documents to “Uniformly μ -continuous topologies on Köthe-Bochner spaces and Orlicz-Bochner spaces”

Topological dual of non-locally convex Orlicz-Bochner spaces

Marian Nowak (1999)

Commentationes Mathematicae Universitatis Carolinae

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Let L ϕ ( X ) be an Orlicz-Bochner space defined by an Orlicz function ϕ taking only finite values (not necessarily convex) over a σ -finite atomless measure space. It is proved that the topological dual L ϕ ( X ) * of L ϕ ( X ) can be represented in the form: L ϕ ( X ) * = L ϕ ( X ) n L ϕ ( X ) s , where L ϕ ( X ) n and L ϕ ( X ) s denote the order continuous dual and the singular dual of L ϕ ( X ) respectively. The spaces L ϕ ( X ) * , L ϕ ( X ) n and L ϕ ( 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...

Inductive limit topologies on Orlicz spaces

Marian Nowak (1991)

Commentationes Mathematicae Universitatis Carolinae

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Let L ϕ be an Orlicz space defined by a convex Orlicz function ϕ and let E ϕ be the space of finite elements in L ϕ (= the ideal of all elements of order continuous norm). We show that the usual norm topology 𝒯 ϕ on L ϕ restricted to E ϕ can be obtained as an inductive limit topology with respect to some family of other Orlicz spaces. As an application we obtain a characterization of continuity of linear operators defined on E ϕ .

Order continuous seminorms and weak compactness in Orlicz spaces.

Marian Nowak (1993)

Collectanea Mathematica

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Let L-phi be an Orlicz space defined by a Young function phi over a sigma-finite measure space, and let phi* denote the complementary function in the sense of Young. We give a characterization of the Mackey topology tau(L*,L-phi*) in terms of some family of norms defined by some regular Young functions. Next we describe order continuous (=absolutely continuous) Riesz seminorms on L-phi, and obtain a criterion for relative sigma(L-phi,L-phi*)-compactness in L-phi. As an application we...