Inductive limit topologies on Orlicz spaces

Marian Nowak

Commentationes Mathematicae Universitatis Carolinae (1991)

  • Volume: 32, Issue: 4, page 667-675
  • ISSN: 0010-2628

Abstract

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Let L ϕ be an Orlicz space defined by a convex Orlicz function ϕ and let E ϕ be the space of finite elements in L ϕ (= the ideal of all elements of order continuous norm). We show that the usual norm topology 𝒯 ϕ on L ϕ restricted to E ϕ 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 ϕ .

How to cite

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Nowak, Marian. "Inductive limit topologies on Orlicz spaces." Commentationes Mathematicae Universitatis Carolinae 32.4 (1991): 667-675. <http://eudml.org/doc/247303>.

@article{Nowak1991,
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 $\mathcal \{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 $.},
author = {Nowak, Marian},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Orlicz spaces; inductive limit topologies; convex functions; inclusions and equalities among Orlicz spaces; Young functions},
language = {eng},
number = {4},
pages = {667-675},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Inductive limit topologies on Orlicz spaces},
url = {http://eudml.org/doc/247303},
volume = {32},
year = {1991},
}

TY - JOUR
AU - Nowak, Marian
TI - Inductive limit topologies on Orlicz spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1991
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 32
IS - 4
SP - 667
EP - 675
AB - 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 $\mathcal {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 $.
LA - eng
KW - Orlicz spaces; inductive limit topologies; convex functions; inclusions and equalities among Orlicz spaces; Young functions
UR - http://eudml.org/doc/247303
ER -

References

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  2. Davis H.W., Murray F.J., Weber J.K., Inductive and projective limits of L p -spaces, Portugal. Math. 38 (1972), 21-29. (1972) Zbl0238.46033MR0303276
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  6. Musielak J., Orlicz W., Some remarks on modular spaces, Bull. Acad. Pol. Sci. 7 (1959), 661-668. (1959) Zbl0099.09202MR0112017
  7. Nowak M., Some equalities among Orlicz spaces II, Bull. Acad. Pol. Sci. 34 (1986), 675-687. (1986) Zbl0639.46033MR0890613
  8. Nowak M., Unions and intersections of families of L p -spaces, Math. Nachr. 136 (1988), 241-251. (1988) MR0952476
  9. Nowak M., Some equalities among Orlicz spaces I, Comment. Math. 29 (1990), 255-275. (1990) Zbl0742.46014MR1059131
  10. Robertson A.P., Robertson W.J., Topological Vector Spaces, Cambridge, 1973. Zbl0423.46001MR0350361
  11. Turpin Ph., Convexités dans les espaces vectoriels topologiques généraux, Dissertationes Math. 131 (1976). (1976) Zbl0331.46001MR0423044
  12. Welland R., Inclusions relations among Orlicz spaces, Proc. Amer. Math. Soc. 17 (1966), 135-138. (1966) MR0188773

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