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

Ihab Al Alam; Georges Habib; Pascal Lefèvre; Fares Maalouf

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

Functional Analysis 2016-12-13 v1

Authors: Ihab Al Alam , Georges Habib , Pascal Lefèvre , Fares Maalouf

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 $1/2$ .

Keywords

Volterra operator Cesàro operator Müntz space essential norm compact operator

Cite

@article{arxiv.1612.03218,
  title  = {Essential norms of Volterra and Ces\`aro operators on M\"untz spaces},
  author = {Ihab Al Alam and Georges Habib and Pascal Lefèvre and Fares Maalouf},
  journal= {arXiv preprint arXiv:1612.03218},
  year   = {2016}
}

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