Inductive limit topologies on Orlicz spaces
Nowak, Marian
Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991), p. 667-675 / Harvested from Czech Digital Mathematics Library
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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 $.

Publié le : 1991-01-01
Classification:  46A13,  46E30,  54A10 
@article{118446,
     author = {Marian Nowak},
     title = {Inductive limit topologies on Orlicz spaces},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {32},
     year = {1991},
     pages = {667-675},
     zbl = {0756.46014},
     mrnumber = {1159813},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118446}
}

Nowak, Marian. Inductive limit topologies on Orlicz spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) pp. 667-675. http://gdmltest.u-ga.fr/item/118446/

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