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

TL;DR

This paper investigates the essential norms of Volterra and Cesàro operators on M"untz spaces, revealing they are non-compact with an essential norm of 1/2, independent of the defining sequence.

Contribution

It provides the first explicit calculation of the essential norm for these operators on M"untz spaces, showing their non-compactness and independence from the sequence mbda.

Findings

Essential norm of 1/2 for both operators

Operators are neither compact nor weakly compact

Essential norm does not depend on mbda

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 $1/2$.