Packing constant for Cesàro-Orlicz sequence spaces

Zhen-Hua Ma; Li-Ning Jiang; Qiao-Ling Xin

Czechoslovak Mathematical Journal (2016)

  • Volume: 66, Issue: 1, page 13-25
  • ISSN: 0011-4642

Abstract

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The packing constant is an important and interesting geometric parameter of Banach spaces. Inspired by the packing constant for Orlicz sequence spaces, the main purpose of this paper is calculating the Kottman constant and the packing constant of the Cesàro-Orlicz sequence spaces ( ces φ ) defined by an Orlicz function φ equipped with the Luxemburg norm. In order to compute the constants, the paper gives two formulas. On the base of these formulas one can easily obtain the packing constant for the Cesàro sequence space ces p and some other sequence spaces. Finally, a new constant D ˜ ( X ) , which seems to be relevant to the packing constant, is given.

How to cite

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Ma, Zhen-Hua, Jiang, Li-Ning, and Xin, Qiao-Ling. "Packing constant for Cesàro-Orlicz sequence spaces." Czechoslovak Mathematical Journal 66.1 (2016): 13-25. <http://eudml.org/doc/276806>.

@article{Ma2016,
abstract = {The packing constant is an important and interesting geometric parameter of Banach spaces. Inspired by the packing constant for Orlicz sequence spaces, the main purpose of this paper is calculating the Kottman constant and the packing constant of the Cesàro-Orlicz sequence spaces ($\{\rm ces\}_\{\phi \}$) defined by an Orlicz function $\phi $ equipped with the Luxemburg norm. In order to compute the constants, the paper gives two formulas. On the base of these formulas one can easily obtain the packing constant for the Cesàro sequence space $\{\rm ces\}_\{p\}$ and some other sequence spaces. Finally, a new constant $\widetilde\{D\}(X)$, which seems to be relevant to the packing constant, is given.},
author = {Ma, Zhen-Hua, Jiang, Li-Ning, Xin, Qiao-Ling},
journal = {Czechoslovak Mathematical Journal},
keywords = {packing constant; Cesàro sequence space; Cesàro-Orlicz sequence space},
language = {eng},
number = {1},
pages = {13-25},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Packing constant for Cesàro-Orlicz sequence spaces},
url = {http://eudml.org/doc/276806},
volume = {66},
year = {2016},
}

TY - JOUR
AU - Ma, Zhen-Hua
AU - Jiang, Li-Ning
AU - Xin, Qiao-Ling
TI - Packing constant for Cesàro-Orlicz sequence spaces
JO - Czechoslovak Mathematical Journal
PY - 2016
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 66
IS - 1
SP - 13
EP - 25
AB - The packing constant is an important and interesting geometric parameter of Banach spaces. Inspired by the packing constant for Orlicz sequence spaces, the main purpose of this paper is calculating the Kottman constant and the packing constant of the Cesàro-Orlicz sequence spaces (${\rm ces}_{\phi }$) defined by an Orlicz function $\phi $ equipped with the Luxemburg norm. In order to compute the constants, the paper gives two formulas. On the base of these formulas one can easily obtain the packing constant for the Cesàro sequence space ${\rm ces}_{p}$ and some other sequence spaces. Finally, a new constant $\widetilde{D}(X)$, which seems to be relevant to the packing constant, is given.
LA - eng
KW - packing constant; Cesàro sequence space; Cesàro-Orlicz sequence space
UR - http://eudml.org/doc/276806
ER -

References

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  1. Burlak, J. A. C., Rankin, R. A., Robertson, A. P., 10.1017/S2040618500033797, Proc. Glasg. Math. Assoc. 4 (1958), 22-25. (1958) MR0119151DOI10.1017/S2040618500033797
  2. Chen, S., Geometry of Orlicz Spaces, With a preface by Julian Musielak Dissertationes Math. (Rozprawy Mat.) 356 (1996), 204. (1996) Zbl1089.46500MR1410390
  3. Cui, Y., Hudzik, H., 10.1016/S0362-546X(01)00389-3, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 47 (2001), 2695-2702. (2001) Zbl1042.46505MR1972393DOI10.1016/S0362-546X(01)00389-3
  4. Cui, Y., Hudzik, H., On the banach-saks and weak banach-saks properties of some banach sequence spaces, Acta Sci. Math. 65 (1999), 179-187. (1999) MR1702144
  5. Cui, Y., Hudzik, H., Petrot, N., Suantai, S., Szymaszkiewicz, A., 10.1007/BF02829808, Proc. Indian Acad. Sci., Math. Sci. 115 (2005), 461-476. (2005) MR2184206DOI10.1007/BF02829808
  6. Foralewski, P., Hudzik, H., Szymaszkiewicz, A., Some remarks on cesàro-orlicz sequence spaces, Math. Inequal. Appl. 13 (2010), 363-386. (2010) Zbl1198.46017MR2662025
  7. Foralewski, P., Hudzik, H., Szymaszkiewicz, A., 10.1016/j.jmaa.2008.04.016, J. Math. Anal. Appl. 345 (2008), 410-419. (2008) Zbl1155.46007MR2422661DOI10.1016/j.jmaa.2008.04.016
  8. Hudzik, H., Every nonreflexive banach lattice has the packing constant equal to 1 / 2 , Collect. Math. 44 (1993), 129-134. (1993) MR1280732
  9. Kottman, C. A., 10.1090/S0002-9947-1970-0265918-7, Trans. Am. Math. Soc. 150 (1970), 565-576. (1970) MR0265918DOI10.1090/S0002-9947-1970-0265918-7
  10. Kubiak, D., 10.1016/j.jmaa.2008.08.022, J. Math. Anal. Appl. 349 (2009), 291-296. (2009) Zbl1160.46013MR2455750DOI10.1016/j.jmaa.2008.08.022
  11. Lee, P. Y., Cesàro sequence spaces, Math. Chron. 13 (1984), 29-45. (1984) Zbl0568.46006MR0769798
  12. Lim, S. K., Lee, P. Y., An orlicz extension of cesàro sequence spaces, Ann. Soc. Math. Pol., Ser. I, Commentat. Math. 28 (1988), 117-128. (1988) MR0988964
  13. Luxemburg, W. A. J., Banach Function Spaces, Thesis Technische Hogeschool te Delft (1955). (1955) MR0072440
  14. Ma, Z., Cui, Y., Some important geometric properties in cesàro-orlicz sequence spaces, Adv. Math., Beijing 42 (2013), 348-354. (2013) Zbl1299.46017MR3144140
  15. Maligranda, L., Orlicz Spaces and Interpolation, Seminars in Mathematics 5 Univ. Estadual de Campinas, Dep. de Matemática, Campinas (1989). (1989) Zbl0874.46022MR2264389
  16. Maligranda, L., Petrot, N., Suantai, S., 10.1016/j.jmaa.2006.02.085, J. Math. Anal. Appl. 326 (2007), 312-331. (2007) MR2277785DOI10.1016/j.jmaa.2006.02.085
  17. Musielak, J., Orlicz Spaces and Modular Spaces, Lecture Notes in Mathematics 1034 Springer, Berlin (1983). (1983) Zbl0557.46020MR0724434
  18. Rankin, R. A., 10.1017/S2040618500033220, Proc. Glasg. Math. Assoc. 2 (1955), 145-146. (1955) MR0074014DOI10.1017/S2040618500033220
  19. Saejung, S., 10.1016/j.jmaa.2010.01.029, J. Math. Anal. Appl. 366 (2010), 530-537. (2010) Zbl1203.46008MR2600499DOI10.1016/j.jmaa.2010.01.029
  20. Webb, J. R. L., Zhao, W., 10.1112/blms/22.5.471, Bull. Lond. Math. Soc. 22 (1990), 471-477. (1990) MR1082019DOI10.1112/blms/22.5.471
  21. Wu, C. X., Lin, P., Piao, Q. Y., Lee, P. Y., Sequence Space and Its Application, Harbin Institute of Technology Press Chinese (2001). (2001) 

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