The Cesàro operator in the Fréchet spaces $ell^{p+}$ and $L^{p-}$

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Abstract

The classical spaces $ell^{p+}$, $1leq p<infty$, and $L^{p−}$, $1<pleqinfty$, are countably normed, reflexive Fréchet spaces in which the Cesàro operator C acts continuously. A detailed investigation is made of various operator theoretic properties of C (e.g., spectrum, point spectrum, mean ergodicity) as well as certain aspects concerning the dynamics of C (e.g., hypercyclic, supercyclic, chaos). This complements the results of [3, 4], where C was studied in the spaces ${mathbb C}^{mathbb N}$, $L^p_{loc}({mathbb R}^+)$ for $1<p<infty$ and $C({mathbb R}^+)$, which belong to a very different collection of Fréchet spaces, called quojections; these are automatically Banach spaces whenever they admit a continuous norm.

Autore Pugliese

Tutti gli autori

  • Albanese A. A. , Bonet J.´ , Ricker W. J.

Titolo volume/Rivista

GLASGOW MATHEMATICAL JOURNAL

Anno di pubblicazione

2017

ISSN

0017-0895

ISBN

Non Disponibile

Numero di citazioni Wos

Nessuna citazione

Ultimo Aggiornamento Citazioni

Non Disponibile

Numero di citazioni Scopus

3

Ultimo Aggiornamento Citazioni

25/04/2018

Settori ERC

Non Disponibile

Codici ASJC

Non Disponibile