Banach Journal of Mathematical Analysis
- Banach J. Math. Anal.
- Volume 10, Number 1 (2016), 1-14.
Geometric properties of the second-order Cesàro spaces
We prove that, for any , the second-order Cesàro sequence space has the -property and the -NUC property for . In addition, we show that has the Kadec–Klee, rotundity, and uniform convexity properties. For any positive integer , we also investigate the uniform Opial and properties of the sequence space. We also establish that is reflexive and has the fixed-point property. Finally, we calculate the packing constant of the space.
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
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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
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