Order continuous linear functionals on non-locally convex Orlicz spaces
Commentationes Mathematicae Universitatis Carolinae (1992)
- Volume: 33, Issue: 3, page 465-475
- ISSN: 0010-2628
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topNowak, Marian. "Order continuous linear functionals on non-locally convex Orlicz spaces." Commentationes Mathematicae Universitatis Carolinae 33.3 (1992): 465-475. <http://eudml.org/doc/247364>.
@article{Nowak1992,
abstract = {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.},
author = {Nowak, Marian},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Orlicz spaces; modular spaces; locally solid Riesz spaces; Köthe dual; order continuous linear functionals; modular spaces; locally solid Riesz spaces; Köthe dual; order continuous linear functionals on an Orlicz space},
language = {eng},
number = {3},
pages = {465-475},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Order continuous linear functionals on non-locally convex Orlicz spaces},
url = {http://eudml.org/doc/247364},
volume = {33},
year = {1992},
}
TY - JOUR
AU - Nowak, Marian
TI - Order continuous linear functionals on non-locally convex Orlicz spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1992
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 33
IS - 3
SP - 465
EP - 475
AB - 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.
LA - eng
KW - Orlicz spaces; modular spaces; locally solid Riesz spaces; Köthe dual; order continuous linear functionals; modular spaces; locally solid Riesz spaces; Köthe dual; order continuous linear functionals on an Orlicz space
UR - http://eudml.org/doc/247364
ER -
References
top- Aliprantis C.D., Burkinshaw O., Locally Solid Riesz Spaces, Academic Press, New York, 1978. Zbl1043.46003MR0493242
- Birnbaum Z., Orlicz W., Über die Verallgemeinerung des Begriffes der zueinander Konjugierten Potenzen, Studia Math. 3 (1931), 1-67. (1931) Zbl0003.25202
- Day M.M., The space with , Bull. Amer. Math. Soc. 46 (1940), 816-823. (1940) MR0002700
- Drewnowski L., Compact operators on Musielak-Orlicz spaces, Comment. Math. 27 (1988), 225-232. (1988) Zbl0676.46024MR0978274
- Gramsch B., Die Klasse metrischer linearer Räume , Math. Ann. 176 (1967), 61-78. (1967) MR0209819
- Kalton N.J., Compact and strictly singular operators on Orlicz spaces, Israel J. Math. 26 (1977), 126-136. (1977) Zbl0348.47016MR0636121
- Kantorovich L.V., Akilov G.P., Functional Analysis (in Russian), Moscow, 1984. MR0788496
- Krasnoselskii M., Rutickii Ya.B., Convex Functions and Orlicz spaces, P. Noordhoff Ltd., Groningen, 1961. MR0126722
- Luxemburg W.A., Banach Function Spaces, Delft, 1955. Zbl0162.44701MR0072440
- Luxemburg W.A., Zaanen A.C., Conjugate spaces of Orlicz spaces, Indagationes Math. 59 (1956), 217-228. (1956) Zbl0072.12301MR0077899
- Maligranda L., Wnuk W., Landau type theorem for Orlicz spaces, Math. Zeitschrift 208 (1991), 57-64. (1991) Zbl0738.46013MR1125732
- Matuszewska W., Orlicz W., A note on the theory of -normed spaces of -integrable functions, Studia Math. 21 (1968), 801-808. (1968) MR0149260
- Musielak J., Orlicz W., Some remarks on modular spaces, Bull. Acad. Polon. Sci. 7 (1959), 661-668. (1959) Zbl0099.09202MR0112017
- Musielak J., Waszak A., Linear continuous functionals over some two-modular spaces, Colloquia Math. Soc. János Bolyai 35 (1980), 877-890. (1980) MR0751051
- Nakano H., Modular semi-ordered linear spaces, Maruzen Co. Ltd., Tokyo, 1950. MR0038565
- Nakano H., On generalized modular spaces, Studia Math. 31 (1968), 439-449. (1968) MR0234248
- Nowak M., Duality of non-locally convex Orlicz spaces, to appear. Zbl0801.46029MR1240281
- Nowak M., Orlicz lattices with modular topology I, Comment. Math. Univ. Carolinae 30 (1989), 261-270. (1989) Zbl0679.46021MR1014127
- 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) Zbl0784.46009MR1155516
- Orlicz W., On integral representability of linear functionals over the space of -integrable functions, Bull. Acad. Polon. Sci. 8 (1960), 567-569. (1960) MR0126160
- Orlicz W., A note on modular spaces I, Bull. Acad. Polon. Sci. 9 (1961), 157-162. (1961) Zbl0109.33404MR0131763
- Peressini A., Order topological vector spaces, Harper and Row, New York, London, 1967. MR0227731
- Turpin P., Convexités dans les espaces vectoriels topologiques généraux, Dissertationes Math. 131 (1976). (1976) Zbl0331.46001MR0423044
- Zaanen A.C., Riesz spaces II, North-Holland Publ. Co., Amsterdam, New York, Oxford, 1983. Zbl0519.46001MR0704021
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