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Comptes Rendus Mathématique
Volume 348, n° 9-10
pages 517-520 (mai 2010)
Doi : 10.1016/j.crma.2010.04.003
Received : 26 January 2010 ;  accepted : 8 April 2010
Asymptotic behavior of polynomially bounded operators
Comportement asymptotique des opérateurs polynomialement bornés
 

Heybetkulu S. Mustafayev
Yuzuncu Yıl University, Faculty of Arts and Sciences, Department of Mathematics, 65080, Van, Turkey 

Abstract

Let T be a polynomially bounded operator on a complex Banach space and let   be the smallest uniformly closed (Banach) algebra that contains T and the identity operator. It is shown that for every  ,
limn→∞‖TnS‖=supξσu(T)|Sˆ(ξ)|, where   is the Gelfand transform of S and   is the unitary spectrum of T ;  .

The full text of this article is available in PDF format.
Résumé

Soit T un opérateur polynomialement borné sur un espace de Banach et soit   la plus petite algèbre de Banach uniformement fermé contenant T et l’identité. Il est montré dans cet article que pour tout  ,
limn→∞‖TnS‖=supξσu(T)|Sˆ(ξ)|, où   est la transformée de Gelfand et   est la spectre unitaire de T ;  .

The full text of this article is available in PDF format.


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