Journal of Operator Theory

Volume 47, Issue 1, Winter 2002 pp. 187-196.

On generalized Riesz points

Authors: Robin Harte (1), Woo Young Lee (2), and Lance L. Littlejohn (3)
Author institution: (1) School of Mathematics, Trinity College, Dublin 2, Ireland
(2) Department of Mathematics, Sungkyunkwan University, Suwon 440--746, Korea
(3) Department of Mathematics and Statistics, Utah State University, Logan, UT 84322--3900, USA

Summary: ``Weyl's theorem" for an operator is a statement about the complement in its spectrum of the ``Weyl spectrum", which we shall call ``generalized Riesz points". In this note we observe how Weyl's theorem and its more relaxed relative ``Browder's theorem" do not generally survive under small perturbations.

Keywords: Generalized Riesz points, Weyl's theorem, Browder's theorem, quasinilpotents

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