Marian Nowak
Inductive limit topologies on Orlicz spaces

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

Abstract: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 $.

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

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