Some Geometric Properties of the Duals of Cesàro Sequence Spaces

Abstract

The spaces d(s) are defined for 0 <= s <= infinity. We consider the fundamental geometric properties of the d(s) spaces, isomorphic duals of the Cesaro sequence spaces ces(r) with 1/s + 1/r =1. We prove that for 1 <= s < infinity, the Banach spaces d(s) are Radon-Riesz spaces that are not rotund or smooth. Moreover, we show that the Banach lattice d(1) has Schur's property, just as i1 does. Finally, a characterization of norm totally bounded subsets of d(1) is also given.