Operators near completely polynomially dominated ones and similarity problems

C. Badea (1)

1 LPP - Laboratoire Paul Painlevé - UMR 8524

Let T and C be two Hilbert space operators. We prove that if T is near, in a certain sense, to an operator completely polynomially dominated with a finite bound by C, then T is similar to an operator which is completely polynomially dominated by the direct sum of C and a suitable weighted unilateral shift. Among the applications, a refined Banach space version of Rota similarity theorem is given and partial answers to a problem of K. Davidson and V. Paulsen are obtained. The latter problem concerns CAR-valued Foguel-Hankel operators which are generalizations of the operator considered by G. Pisier in his example of a polynomial bounded operator not similar to a contraction.

Domaines: Analyse fonctionnelle [math.FA]

C. Badea. Operators near completely polynomially dominated ones and similarity problems. J. Operator Th., 2003, 49, pp.3-23. ⟨hal-00012444⟩