On polynomially bounded operators acting on a Banach space
Idioma
en
Article de revue
Este ítem está publicado en
Journal of Functional Analysis. 2005, vol. 225, p. 147-166
Elsevier
Resumen en inglés
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 ...Leer más >
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.< Leer menos
Palabras clave en inglés
spectral synthesis
polynomially bounded operators
Helson and Kronecker sets
spectral synthesis.
Orígen
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