Journal of Operator Theory

Volume 54, Issue 1, Summer 2005 pp. 125-136.

Similarity of perturbations of Hessenberg matrices

Authors: Leonel Robert (1)
Author institution: Department of Mathematics, University of Toronto, 100 St. George Street, Room 4072, Toronto, ON, Canada M5S 3G3

Summary: To every infinite lower Hessenberg matrix

$D$ is associated a linear operator on

$l_2$ . In this paper we prove the similarity of the operator

$D-\Delta$ , where

$\Delta$ belongs to a certain class of compact operators, to the operator

$D-\Delta^\prime$ , where

$\Delta^\prime$ is of rank one. We first consider the case when

$\Delta$ is lower triangular and has finite rank; then we extend this to

$\Delta$ of infinite rank assuming that

$D$ is bounded. We examine the cases when

$D=S^t$ and

$D=(S+S^t)/2$ , where

$S$ denotes the unilateral shift.

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