We consider spaces, called Müntz spaces, of continuous functions on the unit intervall spanned by certain power functions.
We study the properties of the Volterra and Cesàro operators on the L^1-Müntz 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 the latter does not depend on \Lambda and is equal to 1/2.
This is joint work with Ihab Al Alam, Pascal Lefevre and Fares Maalouf.