Convolution in dual Cesàro sequence spaces

We investigate convolution operators in the sequence spaces $d_p$, for $1\le p<\mathrm{\infty }$. These spaces, for $p>1$, arise as dual spaces of the \ces sequence spaces $ce{s}_p$ thoroughly investigated by G.~Bennett. A detailed study is also made of the algebra of those sequences which convolve $d_p$ into $d_p$. It turns out that such multiplier spaces exhibit features which are very different to the classical multiplier spaces of ${\mathrm{\ell }}^p$.