Previous |  Up |  Next


MSC: 46A45, 46B20
Full entry | Fulltext not available (moving wall 24 months)      Feedback
packing constant; Cesàro sequence space; Cesàro-Orlicz sequence space
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.
[1] Burlak, J. A. C., Rankin, R. A., Robertson, A. P.: The packing of spheres in the space $l_{p}$. Proc. Glasg. Math. Assoc. 4 (1958), 22-25. DOI 10.1017/S2040618500033797 | MR 0119151
[2] Chen, S.: Geometry of Orlicz Spaces. With a preface by Julian Musielak Dissertationes Math. (Rozprawy Mat.) 356 (1996), 204. MR 1410390 | Zbl 1089.46500
[3] Cui, Y., Hudzik, H.: Packing constant for cesaro sequence spaces. Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 47 (2001), 2695-2702. DOI 10.1016/S0362-546X(01)00389-3 | MR 1972393
[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. MR 1702144
[5] Cui, Y., Hudzik, H., Petrot, N., Suantai, S., Szymaszkiewicz, A.: Basic topological and geometric properties of cesàro-orlicz spaces. Proc. Indian Acad. Sci., Math. Sci. 115 (2005), 461-476. DOI 10.1007/BF02829808 | MR 2184206
[6] Foralewski, P., Hudzik, H., Szymaszkiewicz, A.: Some remarks on cesàro-orlicz sequence spaces. Math. Inequal. Appl. 13 (2010), 363-386. MR 2662025
[7] Foralewski, P., Hudzik, H., Szymaszkiewicz, A.: Local rotundity structure of cesàro-orlicz sequence spaces. J. Math. Anal. Appl. 345 (2008), 410-419. DOI 10.1016/j.jmaa.2008.04.016 | MR 2422661
[8] Hudzik, H.: Every nonreflexive banach lattice has the packing constant equal to {$1/2$}. Collect. Math. 44 (1993), 129-134. MR 1280732
[9] Kottman, C. A.: Packing and reflexivity in banach spaces. Trans. Am. Math. Soc. 150 (1970), 565-576. DOI 10.1090/S0002-9947-1970-0265918-7 | MR 0265918
[10] Kubiak, D.: A note on cesàro-orlicz sequence spaces. J. Math. Anal. Appl. 349 (2009), 291-296. DOI 10.1016/j.jmaa.2008.08.022 | MR 2455750
[11] Lee, P. Y.: Cesàro sequence spaces. Math. Chron. 13 (1984), 29-45. MR 0769798 | Zbl 0568.46006
[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. MR 0988964
[13] Luxemburg, W. A. J.: Banach Function Spaces. Thesis Technische Hogeschool te Delft (1955). MR 0072440
[14] Ma, Z., Cui, Y.: Some important geometric properties in cesàro-orlicz sequence spaces. Adv. Math., Beijing 42 (2013), 348-354. MR 3144140
[15] Maligranda, L.: Orlicz Spaces and Interpolation. Seminars in Mathematics 5 Univ. Estadual de Campinas, Dep. de Matemática, Campinas (1989). MR 2264389 | Zbl 0874.46022
[16] Maligranda, L., Petrot, N., Suantai, S.: On the james constant and $B$-convexity of cesàro and cesàro-orlicz sequences spaces. J. Math. Anal. Appl. 326 (2007), 312-331. DOI 10.1016/j.jmaa.2006.02.085 | MR 2277785
[17] Musielak, J.: Orlicz Spaces and Modular Spaces. Lecture Notes in Mathematics 1034 Springer, Berlin (1983). MR 0724434 | Zbl 0557.46020
[18] Rankin, R. A.: On packings of spheres in hilbert space. Proc. Glasg. Math. Assoc. 2 (1955), 145-146. DOI 10.1017/S2040618500033220 | MR 0074014
[19] Saejung, S.: Another look at cesàro sequence spaces. J. Math. Anal. Appl. 366 (2010), 530-537. DOI 10.1016/j.jmaa.2010.01.029 | MR 2600499
[20] Webb, J. R. L., Zhao, W.: On connections between set and ball measures of noncompactness. Bull. Lond. Math. Soc. 22 (1990), 471-477. DOI 10.1112/blms/22.5.471 | MR 1082019
[21] Wu, C. X., Lin, P., Piao, Q. Y., Lee, P. Y.: Sequence Space and Its Application. Harbin Institute of Technology Press Chinese (2001).
Partner of
EuDML logo