# Banach-Saks property in some Banach sequence spaces

Yunan Cui; Henryk Hudzik; Ryszard Płuciennik

Annales Polonici Mathematici (1997)

- Volume: 65, Issue: 2, page 193-202
- ISSN: 0066-2216

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topYunan Cui, Henryk Hudzik, and Ryszard Płuciennik. "Banach-Saks property in some Banach sequence spaces." Annales Polonici Mathematici 65.2 (1997): 193-202. <http://eudml.org/doc/269983>.

@article{YunanCui1997,

abstract = {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.},

author = {Yunan Cui, Henryk Hudzik, Ryszard Płuciennik},

journal = {Annales Polonici Mathematici},

keywords = {Banach-Saks property; property (β); nearly uniform convexity; uniform Kadec-Klee property; property (H); Musielak-Orlicz sequence space; property ; Musielak-Orlicz sequence spaces; near uniform convexity; property },

language = {eng},

number = {2},

pages = {193-202},

title = {Banach-Saks property in some Banach sequence spaces},

url = {http://eudml.org/doc/269983},

volume = {65},

year = {1997},

}

TY - JOUR

AU - Yunan Cui

AU - Henryk Hudzik

AU - Ryszard Płuciennik

TI - Banach-Saks property in some Banach sequence spaces

JO - Annales Polonici Mathematici

PY - 1997

VL - 65

IS - 2

SP - 193

EP - 202

AB - 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.

LA - eng

KW - Banach-Saks property; property (β); nearly uniform convexity; uniform Kadec-Klee property; property (H); Musielak-Orlicz sequence space; property ; Musielak-Orlicz sequence spaces; near uniform convexity; property

UR - http://eudml.org/doc/269983

ER -

## References

top- [1] S. Banach and S. Saks, Sur la convergence forte dans les champs ${L}^{p}$, Studia Math. 2 (1930), 51-57. Zbl56.0932.01
- [2] C J. A. Clarkson, Uniformly convex spaces, Trans. Amer. Math. Soc. 40 (1936), 396-414. Zbl0015.35604
- [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. Zbl0236.47053
- [6] M. Denker and H. Hudzik, Uniformly non-${l}_{n}^{(}1)$ Musielak-Orlicz sequence spaces, Proc. Indian Acad. Sci. 101 (2) (1991), 71-86. Zbl0789.46008
- [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. Zbl0607.46011
- [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. Zbl0721.46012
- [10] H R. Huff, Banach spaces which are nearly uniformly convex, Rocky Mountain J. Math. 10 (1980), 473-749. Zbl0505.46011
- [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. Zbl64.0369.01
- [13] A. Kamińska, Flat Orlicz-Musielak sequence spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. 30 (1992), 347-352. Zbl0513.46008
- [14] A. Kamińska, Uniform rotundity of Musielak-Orlicz sequence spaces, J. Approx. Theory 47 (1986), 302-322. Zbl0606.46003
- [15] D. N. Kutzarova, An isomorphic characterization of property (β) of Rolewicz, Note Mat. 10 (1990), 347-354. Zbl0789.46009
- [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. Zbl0785.46013
- [17] L W. A. J. Luxemburg, Banach function spaces, thesis, Delft, 1955. Zbl0068.09204
- [18] M V. Montesinos, Drop property equals reflexivity, Studia Math. 87 (1987), 93-100. Zbl0652.46009
- [19] J. Musielak, Orlicz Spaces and Modular Spaces, Lecture Notes in Math. 1034, Springer, 1983. Zbl0557.46020
- [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. Zbl0724.46032
- [22] R S. Rolewicz, On Δ-uniform convexity and drop property, Studia Math. 87 (1987), 181-191. Zbl0652.46010

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