Copyright © 2009 Fugen Gao and Xiaochun Fang. 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.
An operator is called -quasiclass if for a positive integer , which is a common generalization of quasiclass . In this paper, firstly we prove some inequalities of this class of operators; secondly we prove that if is a -quasiclass operator, then is isoloid and has finite ascent for all complex
number at last we consider the tensor product for -quasiclass operators.