Banach Journal of Mathematical Analysis

Geometric properties of the second-order Cesàro spaces

Naim L. Braha

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


We prove that, for any p(1,), the second-order Cesàro sequence space Ces2(p) has the (β)-property and the k-NUC property for k2. In addition, we show that Ces2(p) has the Kadec–Klee, rotundity, and uniform convexity properties. For any positive integer k, we also investigate the uniform Opial and (L) properties of the sequence space. We also establish that Ces2(p) is reflexive and has the fixed-point property. Finally, we calculate the packing constant (C) of the space.

Article information

Banach J. Math. Anal., Volume 10, Number 1 (2016), 1-14.

Received: 21 September 2014
Accepted: 20 March 2015
First available in Project Euclid: 15 October 2015

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46A45: Sequence spaces (including Köthe sequence spaces) [See also 46B45] 46B45: Banach sequence spaces [See also 46A45] 46A35: Summability and bases [See also 46B15] 46B20: Geometry and structure of normed linear spaces

second-order Cesàro sequence spaces normed sequence spaces rotundity property Kadec–Klee property uniform Opial property $(\beta)$-property $k$-NUC property


Braha, Naim L. Geometric properties of the second-order Cesàro spaces. Banach J. Math. Anal. 10 (2016), no. 1, 1--14. doi:10.1215/17358787-3158414.

Export citation


  • [1] N. L. Braha, Some geometric properties of $N(\lambda,p)$ spaces, J. Inequal. Appl. 2014, art. ID 112.
  • [2] S. Chen, Geometry of Orlicz Spaces, Dissertationes Math. (Rozprawy Mat.) 356, Polish Acad. Sci. Inst. Math., Warsaw, 1996.
  • [3] Y. Cui and H. Hudzik, On the uniform Opial property in some modular sequence spaces, Funct. Approx. Comment. Math. 26 (1998), 93–102.
  • [4] Y. Cui, H. Hudzik, and R. Pluciennik, Banach–Saks property in some Banach sequence spaces, Ann. Polon. Math. 65 (1997), no. 2, 193–202.
  • [5] Y. Cui, C. Meng, and R. Pluciennik, Banach–Saks property and property $(\beta)$ in Cesàro sequence spaces, Southeast Asian Bull. Math. 24 (2000), no. 2, 201–210.
  • [6] J. Diestel, Geometry of Banach Spaces—Selected Topics, Springer, Berlin, 1984.
  • [7] R. Goebel and W. A. Kirk, Topics in Metric Fixed Point Theory, Cambridge Univ. Press, Cambridge, 1990.
  • [8] V. I. Gurariĭ, Differential properties of the convexity moduli of Banach spaces (in Russian), Mat. Issled. 2 (1967), 141–148.
  • [9] C. A. Kottman, Packing and reflexivity in Banach spaces, Trans. Amer. Math. Soc. 150 (1970), 565–576.
  • [10] I. J. Maddox, Spaces of strongly summable sequences, Quart. J. Math. Oxford 18 (1967), 345–355.
  • [11] H. Nakano, Modulared sequence spaces, Proc. Japan Acad. 27 (1951), 508–512.
  • [12] H. Nergiz and F. Basar, Some geometric properties of the domain of the double sequential band matrix $B(\tilde{r},\tilde{s})$ in the sequence space $l(p)^{*}$, Abstr. Appl. Anal. 2013, art. ID 949282.
  • [13] S. Prus, Banach spaces with uniform Opial property, Nonlinear Anal. 8 (1992), no. 8, 697–704.
  • [14] E. Savaş, V. Karakaya, and N. Şimşek, Some $l(p)$-type new sequence spaces and their geometric properties, Abstr. Appl. Anal. 2009, art. ID 696971.
  • [15] S. Simons, The sequence spaces $l(p_{v})$ and $m(p_{v})$, Proc. London Math. Soc. 15 (1965), 422–436.
  • [16] J. S. Shiue, On the Cesàro sequence space, Tamkang J. Math. 1 (1970), no. 1, 19–25.