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Marian Nowak

Inductive limit topologies on Orlicz spaces

Comment.Math.Univ.Carolinae 32,4 (1991) 667-675.

Abstract: LetLϕ be an Orlicz space defined by a convex Orlicz function ϕ and letEϕ be the space of finite elements inLϕ (= the ideal of all elements of order continuous norm). We show that the usual norm topologyTϕ on Lϕ restricted to Eϕ 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 onEϕ.

Keywords: Orlicz spaces, inductive limit topologies, convex functions AMS Subject Classification: 46E30

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