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International Journal of Mathematics and Mathematical Sciences
Volume 2005, Issue 10, Pages 1543-1554
http://dx.doi.org/10.1155/IJMMS.2005.1543

On the eigenvalues which express antieigenvalues

1Department of Mathematics, Indiana University East, Richmond 47374, IN, USA
2Department of Mathematics, University of Colorado, Boulder 80309-0395, CO, USA

Received 9 August 2004; Revised 22 March 2005

Copyright © 2005 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We showed previously that the first antieigenvalue and the components of the first antieigenvectors of an accretive compact normal operator can be expressed either by a pair of eigenvalues or by a single eigenvalue of the operator. In this paper, we pin down the eigenvalues of T that express the first antieigenvalue and the components of the first antieigenvectors. In addition, we will prove that the expressions which state the first antieigenvalue and the components of the first antieigenvectors are unambiguous. Finally, based on these new results, we will develop an algorithm for computing higher antieigenvalues.