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Zawartość
Pełne teksty:
Warianty tytułu
Abstrakty
CONTENTS
Introduction................................................................................................................................5
Preliminaries..............................................................................................................................5
A. Vector lattices......................................................................................................................6
B. Measure theory.................................................................................................................12
Musielak-Orlicz spaces............................................................................................................15
1. Some properties of Musielak-Orlicz spaces.......................................................................15
2. Isomorphisms between Musielak-Orlicz spaces.................................................................20
3. Drewnowski-Orlicz theorem...............................................................................................23
Representations of Orlicz lattices............................................................................................24
4. Basic properties of orthogonal additive modulars and examples of Orlicz lattices.............24
5. The Main Representation Theorem for Orlicz lattices........................................................32
6. Representation of Orlicz lattices by Orlicz spaces.............................................................40
7. Ultraproducts of some Orlicz lattices..................................................................................48
Notes and comments...............................................................................................................57
References..............................................................................................................................61
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne
tom/nr w serii:
235
Liczba stron
62
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCXXXV
Daty
wydano
1984
Twórcy
autor
Bibliografia
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- [2] C. D. Aliprantis, O. Burkinshaw, Minimal topologies and H-spaces, Illinois J. of Math. 24 (1980), 164-172.
- [3] W.J. Claas, Orlicz lattices, Ph. D. Thesis, Leiden 1977.
- [4] W.J. Claas, A. C. Zaanen, Orlicz lattices, Comment. Math, tomus specialis I (1978), 77-93.
- [5] D. Dacunha-Castelle, Sur une théorème de J. L. Krivine concernant la caracterisation des classes d'espaces isomorphes à des espaces d'Orlicz généralisés et des classes voisines, Israel Math. J. 13 (1972), 261-276.
- [6] D. Dacunha-Castelle, J, L. Krivine, Applications des ultraproduits à l'étude des espaces et des algèbres de Banach, Studia Math. 41 (1972), 315-334.
- [7] L. Drewnowski, On subseries convergence in some function spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 22 (1974), 797-803.
- [8] L. Drewnowski, W. Orlicz, A note on modular spaces X, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 16 (1968), 809-814.
- [9] D. H. Fremlin, Topological Riesz spaces and measure theory, Cambridge Univ. Press, London and New York 1974.
- [10] S. Heinrich, Ultraproducts in Banach spaces theory, J. Reine Angew. Math. 313 (1980), 72-104.
- [11] L. V. Kantorovič, G. P. Akilov, Functional analysis (in Russian), Moscow 1977.
- [12] S. Koshi, T. Shimogaki, On quasi-modular spaces, Studia Math. 21 (1961), 15-35.
- [13] A. Kozek, Orlicz spaces of functions with values in Banach spaces, Comment. Math. 19 (1977), 259-288.
- [14] P. Kranz, W. Wnuk, On the representation of Orlicz lattices, Indagationes Math. 43 (1981), 375-383.
- [15] M. A. Krasnosel'skiĭ, Ya. B. Rutickiĭ, Convex functions and Orlicz spaces, Noordhoff, Groningen 1961.
- [16] J. Lamperti, On the isometries of certain function spaces, Pacific J. Math. 8 (1958), 459-466.
- [17] J. Lindenstrauss, L. Tzafriri, Classical Banach spaces I, Springer-Verlag, Berlin-Heidelberg-New York 1977.
- [18] W. A.J. Luxemburg, A. C. Zaanen, Riesz spaces I, North-Holland Publ., Amsterdam 1971.
- [19] W. Matuszewska, Spaces of φ-integrable functions I, II (in Polish) Prace Matera. VI (1961), 121-139, 149-164.
- [20] W. Matuszewska, W. Orlicz, A note on modular spaces V, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 11 (1963), 51-54.
- [21] J. Musielak, Modular spaces (in Polish), Poznan 1978.
- [22] J. Musielak, W. Orlicz, On modular spaces, Studia Math. 18 (1959), 49-65.
- [23] J. Musielak, W. Orlicz, Some remarks on modular spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 7 (1959), 661-668.
- [24] H. Nakano, Modulared semi-ordered linear spaces, Tokyo 1950.
- [25] N.J. Nielsen, On Banach ideals determined by Banach lattices and their applications, Dissertationes Math. 109 (1973).
- [26] W. Orlicz, a note on modular spaces VII, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 12 (1964), 305-309.
- [27] H. H. Schaefer, Banach lattices and positive operators, Springer-Verlag, Heidelberg 1974.
- [28] M. Schreiber, Quelques remarques sur les caractérisations des espaces $L^p$, 0 < p < 1, Ann. Inst. Henri Poincaré 8 (1972), 83-92.
- [29] T. Shimogaki, Note on Orlicz-Birnbaum-Amemiya's theorem, Proc. Japan Academy 33 (1957), 310-313.
- [30] T. Shimogaki, On the structure of quasi-modular spaces, Studia Math. 22 (1963), 251-263.
- [31] R. Sikorski, Real functions I (in Polish), Monografie Matematyczne t. 35, Warsaw 1958.
- [32] R. Sikorski, Boolean algebras, Springer-Verlag, Berlin-Heidelberg-New York 1969.
- [33] W. Wnuk, On a representation theorem for convex Orlicz lattices, Bull Acad. Polon. Sci. Sér. Sci. Math. 28 (1980), 131-135.
- [34] B. Z. Vulikh, Introduction to the theory of partially ordered spaces (in Russian), Moscow 1961.
- [35] M. Wisła, Continuity of the embedding of some Orlicz spaces, Comment. Math, (to appear).
- [36] H. Hahn, A. Rosenthal, Set functions. The University of New Mexico, Albuquerque 1948.
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