Banach Journal of Mathematical Analysis

Geometric properties of the second-order Cesàro spaces

Naim L. Braha

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1444913859

Digital Object Identifier
doi:10.1215/17358787-3158414

Mathematical Reviews number (MathSciNet)
MR3453520

Zentralblatt MATH identifier
1347.46012

Subjects
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

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

Citation

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. https://projecteuclid.org/euclid.bjma/1444913859


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