• English
    • français
  • français 
    • English
    • français
  • Ouvrir une session
Voir le document 
  •   Accueil de DSpace
  • Research Papers (RP)
  • RP-School of Pure and Applied Sciences
  • RP-Department of Mathematics
  • Voir le document
  •   Accueil de DSpace
  • Research Papers (RP)
  • RP-School of Pure and Applied Sciences
  • RP-Department of Mathematics
  • Voir le document
JavaScript is disabled for your browser. Some features of this site may not work without it.

The spectrum of the Cesàro operator on c0(c0)

Thumbnail
Voir/Ouvrir
title (59.50Ko)
Date
1989-01
Auteur
Okutoyi, J. I.
Thorpe, B.
Metadata
Afficher la notice complète
Résumé
In a recent paper [6], the spectrum of the Cesàro operator C on c0 (the space of null sequences of complex numbers with the sup norm) was obtained by finding the eigenvalues of the adjoinoperator on and showing that the operator (C–λI)−1 lies in B(c0) for all λ outside the closure of this set of eigenvalues. In this paper we apply a similar method to find the spectrum of the two-dimensional Cesàro operator on a space of double sequences c0(c0) (defined in §2). We shall introduce a simplification to the proof in [6] by observing that (C – λI)−1, when it exists, is a Hausdorff summability method (see page 288 of [11] for the single variable case on the space of convergent sequences c), and the crux of our proof is to show that the moment constant associated with the method (C – λI)−1 is regular for the space c0(c0) and the set of λ under consideration. It turns out that c0(c0) c0 c0 (see page 237 of [7]) and that the two-dimensional Cesàro operator on c0(c0) is the tensor product C C of the Cesàro operator C on c0. Thus our result gives a direct proof that the spectrum σ(C C) equals σ(C)σ(C), which is a special case of the result of Schechter in [8].
URI
http://ir-library.ku.ac.ke/handle/123456789/9643
Collections
  • RP-Department of Mathematics [82]

Designed by Library ICT Team copyright © 2017 
Contactez-nous | Faire parvenir un commentaire

 

 

Parcourir

Tout DSpaceCommunautés & CollectionsPar date de publicationAuteursTitresSujetsCette collectionPar date de publicationAuteursTitresSujets

Mon compte

Ouvrir une sessionS'inscrire

Designed by Library ICT Team copyright © 2017 
Contactez-nous | Faire parvenir un commentaire