Geodesic
Inductive limit topologies on Orlicz spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) no. 4, pp. 667-675.

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Let $L^\varphi $ be an Orlicz space defined by a convex Orlicz function $\varphi $ and let $E^\varphi $ be the space of finite elements in $L^\varphi $ (= the ideal of all elements of order continuous norm). We show that the usual norm topology $\Cal T_\varphi$ on $L^\varphi $ restricted to $E^\varphi $ 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^\varphi $.
Classification : 46A13, 46E30, 54A10
Keywords: Orlicz spaces; inductive limit topologies; convex functions 
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     title = {Inductive limit topologies on {Orlicz} spaces},
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Nowak, Marian. Inductive limit topologies on Orlicz spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) no. 4, pp. 667-675. http://geodesic.mathdoc.fr/item/CMUC_1991__32_4_a8/