Convolution in dual Ces\`aro sequence spaces

TL;DR

This paper explores convolution operators in dual Cesàro sequence spaces, revealing unique properties of their multiplier spaces compared to classical p spaces, with implications for functional analysis.

Contribution

It provides a detailed analysis of convolution operators in dual Cesàro sequence spaces and characterizes their multiplier spaces, highlighting differences from classical p spaces.

Findings

Multiplier spaces in dual Cesàro spaces differ from classical p spaces

Convolution operators exhibit unique algebraic properties in these spaces

The study enhances understanding of duality and convolution in sequence spaces

Abstract

We investigate convolution operators in the sequence spaces $d_p$, for $1\le p<\infty$. These spaces, for $p>1$, arise as dual spaces of the \ces sequence spaces $ces_p$ 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 $\ell^p$.