Essential norms of Volterra and Cesàro operators on Müntz spaces. (English) Zbl 1502.47049
Summary: We study the properties of the Volterra and Cesàro operators viewed on the \(L^1\)-Müntz space \(M_\varLambda ^1\) with range in the space of continuous functions. These operators are neither compact nor weakly compact. We estimate how far they are from being (weakly) compact by computing their (generalized) essential norm. It turns out that this norm does not depend on \(\varLambda \) and is equal to \(1/2\).
MSC:
| 47B38 | Linear operators on function spaces (general) |
| 47B07 | Linear operators defined by compactness properties |
| 30H99 | Spaces and algebras of analytic functions of one complex variable |
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