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Asymptotic Isometries for Lacunary Müntz Spaces and Applications

  • Loïc Gaillard
  • Pascal LefèvreEmail author
Article
  • 13 Downloads

Abstract

We prove that the normalized sequence \(\big ((p\lambda _n+1)^{1/p}t^{\lambda _n})\big )_{n\in \mathbb {Z}}\) in \(L^p([0,1])\), up to some truncation, is asymptotically isometric to the canonical basis of \(\ell ^p\) if and only if it is almost isometric if and only if \((\lambda _n+1/p)_n\) (resp. \((\lambda _n)_n\)) is a super-lacunary sequence. This extends recent results of the same authors. Similar results occur in C([0, 1]). As a particular application, we get that all the (strict) s-numbers of the classical Cesàro operator on \(L^p\) are equal to \(p'\) when \(p\in (1,+\infty )\).

Notes

Acknowledgements

The second author is partially supported by the Grant ANR-17-CE40-0021 of the French National Research Agency ANR (project Front).

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Laboratoire de Mathématiques de Lens (LML), EA 2462, Fédération CNRS Nord-Pas-de-Calais FR 2956Université d’ArtoisLens CedexFrance

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