One-dimensional perturbations of operators

Joseph Gail Stampfli

Vol. 115 (1984), No. 2, 481–491

DOI: 10.2140/pjm.1984.115.481

Abstract

The purpose of this note is three-fold. First, to show that certain rank one operators of small norm will split off a unitary piece from the shift; second, to apply this technique to the “Berg construction”; and, third, to exhibit a normal operator whose eigenspace structure is drastically altered by the addition of a rank one operator.

Throughout this paper ℒ(ℋ) will denote the algebra of bounded linear operators on a separable Hilbert space ℋ.

Mathematical Subject Classification 2000

Primary: 47A55

Milestones

Received: 31 August 1981

Published: 1 December 1984