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1996-1997 | 65 | 2 | 193-202
Tytuł artykułu

Banach-Saks property in some Banach sequence spaces

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Abstrakty
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It is proved that for any Banach space X property (β) defined by Rolewicz in [22] implies that both X and X* have the Banach-Saks property. Moreover, in Musielak-Orlicz sequence spaces, criteria for the Banach-Saks property, the near uniform convexity, the uniform Kadec-Klee property and property (H) are given.
Twórcy
autor
  • Department of Mathematics, Harbin University of Science and Technology, Xuefu Road 52, 150080 Harbin, China
  • Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Matejki 48/49, 60-769 Poznań, Poland
  • Institute of Mathematics, T. Kotarbiński Pedagogical University, Pl. Słowiański 9, 65-069 Zielona Góra, Poland
Bibliografia
  • [1] S. Banach and S. Saks, Sur la convergence forte dans les champs $L^p$, Studia Math. 2 (1930), 51-57.
  • [2] C J. A. Clarkson, Uniformly convex spaces, Trans. Amer. Math. Soc. 40 (1936), 396-414.
  • [3] S. Chen, Geometry of Orlicz spaces, Dissertationes Math. 356 (1996).
  • [4] Y. A. Cui and H. Hudzik, Maluta coefficient and Opial property in Musielak-Orlicz sequence spaces equipped with the Luxemburg norm, Nonlinear Anal., to appear.
  • [5] J. Daneš, A geometric theorem useful in nonlinear functional analysis, Boll. Un. Mat. Ital. (4) 6 (1972), 369-375.
  • [6] M. Denker and H. Hudzik, Uniformly non-$l_n^(1)$ Musielak-Orlicz sequence spaces, Proc. Indian Acad. Sci. 101 (2) (1991), 71-86.
  • [7] D J. Diestel, Sequences and Series in Banach Spaces, Grad. Texts in Math. 92, Springer, 1984.
  • [8] K. Goebel and T. Sękowski, The modulus of non-compact convexity, Ann. Univ. Mariae Curie-Skłodowska Sect. A 38 (1984), 41-48.
  • [9] H. Hudzik and Y. Ye, Support functionals and smoothness in Musielak-Orlicz sequence spaces equipped with the Luxemburg norm, Comment. Math. Univ. Carolin. 31 (1990), 661-684.
  • [10] H R. Huff, Banach spaces which are nearly uniformly convex, Rocky Mountain J. Math. 10 (1980), 473-749.
  • [11] K M. I. Kadec [M. I. Kadets], The connection between several convexity properties of the unit sphere of a Banach space, Funktsional. Anal. i Prilozhen. 16 (3) (1982), 58-60 (in Russian); English transl.: Functional Anal. Appl. 16 (3) (1982), 204-206.
  • [12] S. Kakutani, Weak convergence in uniformly convex Banach spaces, Tôhoku Math. J. 45 (1938), 188-193.
  • [13] A. Kamińska, Flat Orlicz-Musielak sequence spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. 30 (1992), 347-352.
  • [14] A. Kamińska, Uniform rotundity of Musielak-Orlicz sequence spaces, J. Approx. Theory 47 (1986), 302-322.
  • [15] D. N. Kutzarova, An isomorphic characterization of property (β) of Rolewicz, Note Mat. 10 (1990), 347-354.
  • [16] D. N. Kutzarova, E. Maluta and S. Prus, Property (β) implies normal structure of the dual space, Rend. Circ. Mat. Palermo 41 (1992), 335-368.
  • [17] L W. A. J. Luxemburg, Banach function spaces, thesis, Delft, 1955.
  • [18] M V. Montesinos, Drop property equals reflexivity, Studia Math. 87 (1987), 93-100.
  • [19] J. Musielak, Orlicz Spaces and Modular Spaces, Lecture Notes in Math. 1034, Springer, 1983.
  • [20] P S. Prus, Nearly uniformly smooth Banach spaces, Boll. Un. Mat. Ital. B (7) 3 (1989), 506-521.
  • [21] M. M. Rao and Z. D. Ren, Theory of Orlicz Spaces, Marcel Dekker, New York, 1991.
  • [22] R S. Rolewicz, On Δ-uniform convexity and drop property, Studia Math. 87 (1987), 181-191.
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Bibliografia
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