Comptes Rendus
Mathematical Analysis
Asymptotic behavior of polynomially bounded operators
[Comportement asymptotique des opérateurs polynomialement bornés]
Comptes Rendus. Mathématique, Volume 348 (2010) no. 9-10, pp. 517-520.

Let T be a polynomially bounded operator on a complex Banach space and let AT be the smallest uniformly closed (Banach) algebra that contains T and the identity operator. It is shown that for every SAT,

limnTnS=supξσu(T)|Sˆ(ξ)|,
where Sˆ is the Gelfand transform of S and σu(T):=σ(T)Γ is the unitary spectrum of T; Γ={zC:|z|=1}.

Soit T un opérateur polynomialement borné sur un espace de Banach et soit AT la plus petite algèbre de Banach uniformement fermé contenant T et l'identité. Il est montré dans cet article que pour tout SAT,

limnTnS=supξσu(T)|Sˆ(ξ)|,
Sˆ est la transformée de Gelfand et σu(T):=σ(T)Γ est la spectre unitaire de T ; Γ:={zC:|z|=1}.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2010.04.003

Heybetkulu S. Mustafayev 1

1 Yuzuncu Yıl University, Faculty of Arts and Sciences, Department of Mathematics, 65080, Van, Turkey
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Heybetkulu S. Mustafayev. Asymptotic behavior of polynomially bounded operators. Comptes Rendus. Mathématique, Volume 348 (2010) no. 9-10, pp. 517-520. doi : 10.1016/j.crma.2010.04.003. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.04.003/

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