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In this paper, we introduce a new geometric property in Banach spaces, namely compact midpoint local uniform convexity. Criteria for this property in Orlicz spaces are given for both norms in the function case as well as in the sequence case.
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Rocznik
Tom
Strony
53--62
Opis fizyczny
Bibliogr. 22 poz.
Bibliografia
- [1] S. Chen, Geometry of Orlicz spaces, Dissertationes Mathematical 356 (1996).
- [2] S. Chen, Y. Cui and H. Hudzik, Isometric copies of l1 and l∞ in Orlicz spaces equipped with the Orlicz norm, to appear.
- [3] S. Chen and Y. Wang, H-property of Orlicz spaces, Chinese Ann. Math. 8A (1987), 367-376.
- [4] J. A. Clarkson, Uniformly convex spaces, Trans. Amer. Math. Soc. 40 (1936), 396-414.
- [5] Y. Cui, H. Hudzik, M. Nowak and R. Płuciennik, Some geometric properties in Orlicz sequence spaces equipped with Orlicz norm, Jour. Conv. Anal. 6 (1999), 91-113.
- [6] Y. Cui and T. Wang, Strongly extreme points of Orlicz spaces, J. Math. 7 (4) (1987), 335-340.
- [7] J. Diestel, Geometry of Banach Spaces - Selected Topics, Springer-Verlag, Berlin-New York, 1975.
- [8] M. M. Day, Normed Linear Spaces, 3rd ed., Springer-Verlag, Berlin-New York, 1973.
- [9] Ky Fan and I. Glichsberg, Fully convex normed linear spaces, Proc. Nat. Acad. Sci. USA 41 (1955), 947-953.
- [10] H. Hudzik, Uniformly non-ln(1) Orlicz spaces with Luxemburg norm, Studia Math. 81 (1985), 277-284.
- [11] R. Huff, Banach spaces which are nearly uniformly convex, Rocky Mountain J. Math. 10 (1980), 473-479.
- [12] A. Kamińska, On unifom convexity of Orlicz spaces, Indagationes Math. A85 (1982), 27-36.
- [13] M. A. Krasnoselskii and Ya. B. Rutickii, Convex Functions and Orlicz Spaces, Nordhoff, Groningen, 1961.
- [14] B. L. Lin and W. Y. Zhang, Some Geometric Properties Related to Unifom Convexity of Banach Spaces, Lecture Notes Pure Appl. Math. 136 (1992), 281-293.
- [15] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces, Lecture Notes in Math., 338 (1973).
- [16] W. A. J. Luxemburg, Banach Function Spaces, Thesis, Delft, 1955.
- [17] J. Musielak, Orlicz Spaces and Modular Spaces, Lecture Notes in Math. 1034 (1983), 1-222.
- [18] B. B. Panda and O. P. Kapoor, Generalization of local uniform convexity of the norm, J. Math. Anal. Appl. 52 (1975), 300-308.
- [19] M. M. Rao and Z. D. Ren, Theory of Orlicz Spaces, Marcel Dekker Inc., New York-Basel-Hong-Kong, 1991.
- [20] J. R. Partington, On the Banach-Saks property, Math. Proc. Camb. Phil. Soc. 82 (1977), 369-374.
- [21] T. Wang, Y. Cui and Z. Tao, The Kadec-Klee property in Musielak-Orlicz spaces equipped with the Luxemburg norm, Scientiae Math. 1 (1998), 339-345.
- [22] X. T. Yu, Geometric Theory of Banach Spaces, Huadong Teacher University Press, 1984 (in Chinese).
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Bibliografia
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bwmeta1.element.baztech-article-BUS2-0002-0046