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Keywords:
Orlicz spaces; inductive limit topologies; convex functions
Orlicz spaces; inductive limit topologies; convex functions
Summary:
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 $.
References:
[1] Davis H.W., Murray F.J., Weber J.K.: Families of $L_p$-spaces with inductive and projective topologies. Pacific J. Math. 34 (1970), 619-638. MR 0267389
[2] Davis H.W., Murray F.J., Weber J.K.: Inductive and projective limits of $L_p$-spaces. Portugal. Math. 38 (1972), 21-29. MR 0303276 | Zbl 0238.46033
[3] Krasnoselskii M.A., Rutickii Ya.B.: Convex Functions and Orlicz Spaces. Groningen, 1961.
[4] Leśniewicz R.: On two equalities for Orlicz spaces. Bull. Acad. Pol. Sci. 27 (1979), 557-560. MR 0581551
[5] Luxemburg W.A.: Banach Functions Spaces. Delft, 1955. MR 0072440
[6] Musielak J., Orlicz W.: Some remarks on modular spaces. Bull. Acad. Pol. Sci. 7 (1959), 661-668. MR 0112017 | Zbl 0099.09202
[7] Nowak M.: Some equalities among Orlicz spaces II. Bull. Acad. Pol. Sci. 34 (1986), 675-687. MR 0890613 | Zbl 0639.46033
[8] Nowak M.: Unions and intersections of families of $L^p$-spaces. Math. Nachr. 136 (1988), 241-251. MR 0952476
[9] Nowak M.: Some equalities among Orlicz spaces I. Comment. Math. 29 (1990), 255-275. MR 1059131 | Zbl 0742.46014
[10] Robertson A.P., Robertson W.J.: Topological Vector Spaces. Cambridge, 1973. MR 0350361 | Zbl 0423.46001
[11] Turpin Ph.: Convexités dans les espaces vectoriels topologiques généraux. Dissertationes Math. 131 (1976). MR 0423044 | Zbl 0331.46001
[12] Welland R.: Inclusions relations among Orlicz spaces. Proc. Amer. Math. Soc. 17 (1966), 135-138. MR 0188773
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