Order continuous linear functionals on non-locally convex Orlicz spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) no. 3, pp. 465-475 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

The space of all order continuous linear functionals on an Orlicz space $L^\varphi $ defined by an arbitrary (not necessarily convex) Orlicz function $\varphi $ is described.
The space of all order continuous linear functionals on an Orlicz space $L^\varphi $ defined by an arbitrary (not necessarily convex) Orlicz function $\varphi $ is described.
Classification : 46A80, 46B10, 46B30, 46B42, 46E30
Keywords: Orlicz spaces; modular spaces; locally solid Riesz spaces; Köthe dual; order continuous linear functionals
@article{CMUC_1992_33_3_a8,
     author = {Nowak, Marian},
     title = {Order continuous linear functionals on non-locally convex {Orlicz} spaces},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {465--475},
     year = {1992},
     volume = {33},
     number = {3},
     mrnumber = {1209288},
     zbl = {0812.46017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1992_33_3_a8/}
}
TY  - JOUR
AU  - Nowak, Marian
TI  - Order continuous linear functionals on non-locally convex Orlicz spaces
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 1992
SP  - 465
EP  - 475
VL  - 33
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/CMUC_1992_33_3_a8/
LA  - en
ID  - CMUC_1992_33_3_a8
ER  - 
%0 Journal Article
%A Nowak, Marian
%T Order continuous linear functionals on non-locally convex Orlicz spaces
%J Commentationes Mathematicae Universitatis Carolinae
%D 1992
%P 465-475
%V 33
%N 3
%U http://geodesic.mathdoc.fr/item/CMUC_1992_33_3_a8/
%G en
%F CMUC_1992_33_3_a8
Nowak, Marian. Order continuous linear functionals on non-locally convex Orlicz spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) no. 3, pp. 465-475. http://geodesic.mathdoc.fr/item/CMUC_1992_33_3_a8/

[1] Aliprantis C.D., Burkinshaw O.: Locally Solid Riesz Spaces. Academic Press, New York, 1978. | MR | Zbl

[2] Birnbaum Z., Orlicz W.: Über die Verallgemeinerung des Begriffes der zueinander Konjugierten Potenzen. Studia Math. 3 (1931), 1-67. | Zbl

[3] Day M.M.: The space $L^p$ with $0. Bull. Amer. Math. Soc. 46 (1940), 816-823. MR 0002700

[4] Drewnowski L.: Compact operators on Musielak-Orlicz spaces. Comment. Math. 27 (1988), 225-232. | MR | Zbl

[5] Gramsch B.: Die Klasse metrischer linearer Räume $\mathscr{L}_{\Phi}$. Math. Ann. 176 (1967), 61-78. | MR

[6] Kalton N.J.: Compact and strictly singular operators on Orlicz spaces. Israel J. Math. 26 (1977), 126-136. | MR | Zbl

[7] Kantorovich L.V., Akilov G.P.: Functional Analysis (in Russian). Moscow, 1984. | MR

[8] Krasnoselskii M., Rutickii Ya.B.: Convex Functions and Orlicz spaces. P. Noordhoff Ltd., Groningen, 1961. | MR

[9] Luxemburg W.A.: Banach Function Spaces. Delft, 1955. | MR | Zbl

[10] Luxemburg W.A., Zaanen A.C.: Conjugate spaces of Orlicz spaces. Indagationes Math. 59 (1956), 217-228. | MR | Zbl

[11] Maligranda L., Wnuk W.: Landau type theorem for Orlicz spaces. Math. Zeitschrift 208 (1991), 57-64. | MR | Zbl

[12] Matuszewska W., Orlicz W.: A note on the theory of $s$-normed spaces of $\varphi $-integrable functions. Studia Math. 21 (1968), 801-808. | MR

[13] Musielak J., Orlicz W.: Some remarks on modular spaces. Bull. Acad. Polon. Sci. 7 (1959), 661-668. | MR | Zbl

[14] Musielak J., Waszak A.: Linear continuous functionals over some two-modular spaces. Colloquia Math. Soc. János Bolyai 35 (1980), 877-890. | MR

[15] Nakano H.: Modular semi-ordered linear spaces. Maruzen Co. Ltd., Tokyo, 1950. | MR

[16] Nakano H.: On generalized modular spaces. Studia Math. 31 (1968), 439-449. | MR

[17] Nowak M.: Duality of non-locally convex Orlicz spaces. to appear. | MR | Zbl

[18] Nowak M.: Orlicz lattices with modular topology I. Comment. Math. Univ. Carolinae 30 (1989), 261-270. | MR | Zbl

[19] Nowak M.: Linear functionals on Orlicz sequence spaces without local convexity. Inter. J. for Math. and Math. Sciences 15 , No. 2 (1992), 241-254. | MR | Zbl

[20] Orlicz W.: On integral representability of linear functionals over the space of $\varphi $-integrable functions. Bull. Acad. Polon. Sci. 8 (1960), 567-569. | MR

[21] Orlicz W.: A note on modular spaces I. Bull. Acad. Polon. Sci. 9 (1961), 157-162. | MR | Zbl

[22] Peressini A.: Order topological vector spaces. Harper and Row, New York, London, 1967. | MR

[23] Turpin P.: Convexités dans les espaces vectoriels topologiques généraux. Dissertationes Math. 131 (1976). | MR | Zbl

[24] Zaanen A.C.: Riesz spaces II. North-Holland Publ. Co., Amsterdam, New York, Oxford, 1983. | MR | Zbl