International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 53, Pages 2821-2834

On the Putnam-Fuglede theorem

Yin Chen

Department of Mathematical Sciences, Lakehead University, Thunder Bay P7B 5E1, ON, Canada

Received 25 November 2003

Copyright © 2004 Yin Chen. 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.


We extend the Putnam-Fuglede theorem and the second-degree Putnam-Fuglede theorem to the nonnormal operators and to an elementary operator under perturbation by quasinilpotents. Some asymptotic results are also given.