2001/02/28 by C. Badea
Mathematics · #math.FA #msc:47A30 #msc:46L07
published as J. Operator Th. 49(2003), 3-23. · 22 pages
arxiv created 2002/06/07 · arxiv updated 2009/11/30
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.