International Journal of Mathematics and Mathematical Sciences
Volume 2009 (2009), Article ID 603041, 6 pages
Research Article

A Note on the Range of the Operator XTXXT Defined on 𝒞2()

Department of Mathematics, Florida A&M University, Tallahassee, FL 32307, USA

Received 10 November 2008; Accepted 11 May 2009

Academic Editor: Manfred H. Moller

Copyright © 2009 Vasile Lauric. 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 show how a proof of J. Stampfli can be extended to prove that the operator XTXXT defined on the Hilbert-Schmidt class, when T is an M-hyponormal, p-hyponormal, or log-hyponormal operator, has a closed range if and only if σ(T) is finite.