Multiplier and averaging operators in the Banach spaces ces(p), 1 < p < ∞

The Banach sequence spaces ces(p) are generated in a specified way via the classical spaces p,1<p<. For each pair 1<p,q< the (p,q)-multiplier operators from ces(p) into ces(q) are known. We determine precisely which of these multipliers is a compact operator. Moreover, for the case of p=q a complete description is presented of those (p,p)-multiplier operators which are mean (resp. uniform mean) ergodic. A study is also made of the linear operator C which maps a numerical sequence to the sequence of its averages. All pairs 1<p,q< are identified for which C maps ces(p) into ces(q) and, amongst this collection, those which are compact. For p=q, the mean ergodic properties of C are also treated.