On polynomially bounded operators acting on a Banach space
Langue
en
Article de revue
Ce document a été publié dans
Journal of Functional Analysis. 2005, vol. 225, p. 147-166
Elsevier
Résumé en anglais
By the Von Neumann inequality every contraction on a Hilbert space is polynomially bounded. A simple example shows that this result does not extend to Banach space contractions. In this paper we give general conditions ...Lire la suite >
By the Von Neumann inequality every contraction on a Hilbert space is polynomially bounded. A simple example shows that this result does not extend to Banach space contractions. In this paper we give general conditions under which an arbitrary Banach space contraction is polynomially bounded. These conditions concern the thinness of the spectrum and the behaviour of the resolvent or the sequence of negative powers. To do this we use techniques from harmonic analysis, in particular, results concerning thin sets such as Helson sets, Kronecker sets and sets that satisfy spectral synthesis.< Réduire
Mots clés en anglais
spectral synthesis
polynomially bounded operators
Helson and Kronecker sets
spectral synthesis.
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