Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 584642, 10 pages
doi:10.1155/2010/584642
Research Article

A Note on (𝒞p,α)-Hyponormal Operators

Xiaohuan Wang1 and Zongsheng Gao2

1LMIB and School of Mathematics and Systems Science, Beihang University, Beijing 100191, China
2LMIB and Department of Mathematics, Beihang University, Beijing 100191, China

Received 20 January 2010; Accepted 22 April 2010

Academic Editor: Sin Takahasi

Copyright © 2010 Xiaohuan Wang and Zongsheng Gao. 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 study (𝒞p,α)-normal operators and (𝒞p,α)-hyponormal operators. We show the inclusion relation between these classes under various hypotheses for p and α. We also obtain some sufficient conditions for Aluthge transform T̃s,t=|T|sU|T|t and T2 of (𝒞p,α)-hyponormal operators still to be (𝒞p,α)-hyponormal.