On the H-property of some Banach sequence spaces


Suthep  Suantai

Department of Mathematics, Faculty of Science
Chiang Mai University, Chiang Mai 50200, Thailand

E-mail:  scmti005@chiangmai.ac.th

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.