Order continuous linear functionals on non-locally convex Orlicz spaces
Nowak, Marian
Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992), p. 465-475 / Harvested from Czech Digital Mathematics Library

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.

Publié le : 1992-01-01
Classification:  46A80,  46B10,  46B30,  46B42,  46E30
@article{118514,
     author = {Marian Nowak},
     title = {Order continuous linear functionals on non-locally convex Orlicz spaces},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {33},
     year = {1992},
     pages = {465-475},
     zbl = {0812.46017},
     mrnumber = {1209288},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118514}
}
Nowak, Marian. Order continuous linear functionals on non-locally convex Orlicz spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) pp. 465-475. http://gdmltest.u-ga.fr/item/118514/

Aliprantis C.D.; Burkinshaw O. Locally Solid Riesz Spaces, Academic Press, New York, 1978. | MR 0493242 | Zbl 1043.46003

Birnbaum Z.; Orlicz W. Über die Verallgemeinerung des Begriffes der zueinander Konjugierten Potenzen, Studia Math. 3 (1931), 1-67. (1931) | Zbl 0003.25202

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

Drewnowski L. Compact operators on Musielak-Orlicz spaces, Comment. Math. 27 (1988), 225-232. (1988) | MR 0978274 | Zbl 0676.46024

Gramsch B. Die Klasse metrischer linearer Räume $\mathscr{L}_{\Phi}$, Math. Ann. 176 (1967), 61-78. (1967) | MR 0209819

Kalton N.J. Compact and strictly singular operators on Orlicz spaces, Israel J. Math. 26 (1977), 126-136. (1977) | MR 0636121 | Zbl 0348.47016

Kantorovich L.V.; Akilov G.P. Functional Analysis (in Russian), Moscow, 1984. | MR 0788496

Krasnoselskii M.; Rutickii Ya.B. Convex Functions and Orlicz spaces, P. Noordhoff Ltd., Groningen, 1961. | MR 0126722

Luxemburg W.A. Banach Function Spaces, Delft, 1955. | MR 0072440 | Zbl 0162.44701

Luxemburg W.A.; Zaanen A.C. Conjugate spaces of Orlicz spaces, Indagationes Math. 59 (1956), 217-228. (1956) | MR 0077899 | Zbl 0072.12301

Maligranda L.; Wnuk W. Landau type theorem for Orlicz spaces, Math. Zeitschrift 208 (1991), 57-64. (1991) | MR 1125732 | Zbl 0738.46013

Matuszewska W.; Orlicz W. A note on the theory of $s$-normed spaces of $\varphi $-integrable functions, Studia Math. 21 (1968), 801-808. (1968) | MR 0149260

Musielak J.; Orlicz W. Some remarks on modular spaces, Bull. Acad. Polon. Sci. 7 (1959), 661-668. (1959) | MR 0112017 | Zbl 0099.09202

Musielak J.; Waszak A. Linear continuous functionals over some two-modular spaces, Colloquia Math. Soc. János Bolyai 35 (1980), 877-890. (1980) | MR 0751051

Nakano H. Modular semi-ordered linear spaces, Maruzen Co. Ltd., Tokyo, 1950. | MR 0038565

Nakano H. On generalized modular spaces, Studia Math. 31 (1968), 439-449. (1968) | MR 0234248

Nowak M. Duality of non-locally convex Orlicz spaces, to appear. | MR 1240281 | Zbl 0801.46029

Nowak M. Orlicz lattices with modular topology I, Comment. Math. Univ. Carolinae 30 (1989), 261-270. (1989) | MR 1014127 | Zbl 0679.46021

Nowak M. Linear functionals on Orlicz sequence spaces without local convexity, Inter. J. for Math. and Math. Sciences 15 , No. 2 (1992), 241-254. (1992) | MR 1155516 | Zbl 0784.46009

Orlicz W. On integral representability of linear functionals over the space of $\varphi $-integrable functions, Bull. Acad. Polon. Sci. 8 (1960), 567-569. (1960) | MR 0126160

Orlicz W. A note on modular spaces I, Bull. Acad. Polon. Sci. 9 (1961), 157-162. (1961) | MR 0131763 | Zbl 0109.33404

Peressini A. Order topological vector spaces, Harper and Row, New York, London, 1967. | MR 0227731

Turpin P. Convexités dans les espaces vectoriels topologiques généraux, Dissertationes Math. 131 (1976). (1976) | MR 0423044 | Zbl 0331.46001

Zaanen A.C. Riesz spaces II, North-Holland Publ. Co., Amsterdam, New York, Oxford, 1983. | MR 0704021 | Zbl 0519.46001