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Keywords:
Orlicz spaces; modular spaces; locally solid Riesz spaces; Köthe dual; order continuous linear functionals
Orlicz spaces; modular spaces; locally solid Riesz spaces; Köthe dual; order continuous linear functionals
Summary:
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.
References:
[1] Aliprantis C.D., Burkinshaw O.: Locally Solid Riesz Spaces. Academic Press, New York, 1978. MR 0493242 | Zbl 1043.46003
[2] Birnbaum Z., Orlicz W.: Über die Verallgemeinerung des Begriffes der zueinander Konjugierten Potenzen. Studia Math. 3 (1931), 1-67. Zbl 0003.25202
[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 0978274 | Zbl 0676.46024
[5] Gramsch B.: Die Klasse metrischer linearer Räume $\mathscr{L}_{\Phi}$. Math. Ann. 176 (1967), 61-78. MR 0209819
[6] Kalton N.J.: Compact and strictly singular operators on Orlicz spaces. Israel J. Math. 26 (1977), 126-136. MR 0636121 | Zbl 0348.47016
[7] Kantorovich L.V., Akilov G.P.: Functional Analysis (in Russian). Moscow, 1984. MR 0788496
[8] Krasnoselskii M., Rutickii Ya.B.: Convex Functions and Orlicz spaces. P. Noordhoff Ltd., Groningen, 1961. MR 0126722
[9] Luxemburg W.A.: Banach Function Spaces. Delft, 1955. MR 0072440 | Zbl 0162.44701
[10] Luxemburg W.A., Zaanen A.C.: Conjugate spaces of Orlicz spaces. Indagationes Math. 59 (1956), 217-228. MR 0077899 | Zbl 0072.12301
[11] Maligranda L., Wnuk W.: Landau type theorem for Orlicz spaces. Math. Zeitschrift 208 (1991), 57-64. MR 1125732 | Zbl 0738.46013
[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 0149260
[13] Musielak J., Orlicz W.: Some remarks on modular spaces. Bull. Acad. Polon. Sci. 7 (1959), 661-668. MR 0112017 | Zbl 0099.09202
[14] Musielak J., Waszak A.: Linear continuous functionals over some two-modular spaces. Colloquia Math. Soc. János Bolyai 35 (1980), 877-890. MR 0751051
[15] Nakano H.: Modular semi-ordered linear spaces. Maruzen Co. Ltd., Tokyo, 1950. MR 0038565
[16] Nakano H.: On generalized modular spaces. Studia Math. 31 (1968), 439-449. MR 0234248
[17] Nowak M.: Duality of non-locally convex Orlicz spaces. to appear. MR 1240281 | Zbl 0801.46029
[18] Nowak M.: Orlicz lattices with modular topology I. Comment. Math. Univ. Carolinae 30 (1989), 261-270. MR 1014127 | Zbl 0679.46021
[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 1155516 | Zbl 0784.46009
[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 0126160
[21] Orlicz W.: A note on modular spaces I. Bull. Acad. Polon. Sci. 9 (1961), 157-162. MR 0131763 | Zbl 0109.33404
[22] Peressini A.: Order topological vector spaces. Harper and Row, New York, London, 1967. MR 0227731
[23] Turpin P.: Convexités dans les espaces vectoriels topologiques généraux. Dissertationes Math. 131 (1976). MR 0423044 | Zbl 0331.46001
[24] Zaanen A.C.: Riesz spaces II. North-Holland Publ. Co., Amsterdam, New York, Oxford, 1983. MR 0704021 | Zbl 0519.46001
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