E-mail: scmti005@chiangmai.ac.th
Abstract.
In this paper we define a generalized Cesaro
sequence space $ces(p)$ and consider it equipped with the Luxemburg
norm
under which it is a Banach space, and we show that the space
$ces(p)$ posses
property (H) and property (G), and it is rotund, where
$p = (p_k)$ is a bounded
sequence of positive real numbers with $p_k > 1$ for all $k \in
\Bbb N$.
AMSclassification. 46E30, 46E40, 46B20
Keywords. H-property, property (G), Ces\`{a}ro sequence spaces, Luxemburg norm.