Convolution in dual Cesàro sequence spaces

Abstract

We investigate convolution operators in the sequence spaces dp, for 1≤p<∞. These spaces, for p>1, arise as dual spaces of the Cesàro sequence spaces cesp thoroughly investigated by G. Bennett. A detailed study is also made of the algebra of those sequences which convolve dp into dp. It turns out that such multiplier spaces exhibit features which are very different to the classical multiplier spaces of ℓp.