Some geometric properties of generalized difference Cesàro sequence spaces

Abstract

In this paper, we define the generalized Cesàro difference sequence space C(p) (?m) and consider it equipped with the Luxemburg normunder which it is a Banach space and we show that in the space C(p) (?m) every weakly convergent sequence on the unit sphere converges is the norm, where p = (pn) is a bounded sequence of positive real numbers with pn > 1 for all n ? N. © 2017 by the Mathematical Association of Thailand. All rights reserved.