arXiv math/01021602001-02math.FA

Operators near completely polynomially dominated ones and similarity problems

C. Badea

备注：: 22 pages
发表信息：: J. Operator Th. 49(2003), 3-23.

英文摘要：

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.

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