Geometric properties of the second-order Cesàro spaces

Abstract

We prove that, for any $p\in (1,\infty )$, the second-order Cesàro sequence space ${Ces}^2\left(p\right)$ has the $\left(\beta \right)$-property and the $k$-NUC property for $k\ge 2$. In addition, we show that ${Ces}^2\left(p\right)$ has the Kadec–Klee, rotundity, and uniform convexity properties. For any positive integer $k$, we also investigate the uniform Opial and $\left(L\right)$ properties of the sequence space. We also establish that ${Ces}^2\left(p\right)$ is reflexive and has the fixed-point property. Finally, we calculate the packing constant $\left(C\right)$ of the space.