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.
We study -normal operators and -hyponormal operators. We show the inclusion relation between these classes under various hypotheses for and . We also obtain some sufficient conditions for Aluthge transform and of -hyponormal operators still to be -hyponormal.