International Journal of Mathematics and Mathematical Sciences
Volume 2011 (2011), Article ID 801313, 5 pages
http://dx.doi.org/10.1155/2011/801313
Research Article

Almost 𝜶 -Hyponormal Operators with Weyl Spectrum of Area Zero

Vasile Lauric

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

Received 27 December 2010; Accepted 20 March 2011

Academic Editor: Raül Curto

Copyright © 2011 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.

Abstract

We define the class of almost 𝛼 -hyponormal operators and prove that for an operator 𝑇 in this class, ( 𝑇 ∗ 𝑇 ) 𝛼 − ( 𝑇 𝑇 ∗ ) 𝛼 is trace-class and its trace is zero when 𝛼 ∈ ( 0 , 1 ] and the area of the Weyl spectrum is zero.