Essential norms of Volterra and Ces\`aro operators on M\"untz spaces

Abstract

We study the properties of the Volterra and Ces\`aro operators viewed on the $L^1$-M\"untz space $M_\Lambda^1$ with range in the space of continuous functions. These operators are neither compact nor weakly compact. We estimate how far from being (weakly) compact they are by computing their (generalized) essential norm. It turns out that this latter does not depend on $\Lambda$ and is equal to $1/2$.