Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 921634, 10 pages
doi:10.1155/2009/921634
Research Article

On k-Quasiclass A Operators

Fugen Gao1,2 and Xiaochun Fang1

1Department of Mathematics, Tongji University, Shanghai 200092, China
2College of Mathematics and Information Science, Henan Normal University, Xinxiang, Henan 453007, China

Received 26 June 2009; Revised 6 September 2009; Accepted 10 November 2009

Academic Editor: Sin-Ei Takahasi

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.

Abstract

An operator T∈B(ℋ) is called k-quasiclass A if T∗k(|T2|−|T|2)Tk≥0 for a positive integer k, which is a common generalization of quasiclass A. In this paper, firstly we prove some inequalities of this class of operators; secondly we prove that if T is a k-quasiclass A operator, then T is isoloid and T−λ has finite ascent for all complex number λ; at last we consider the tensor product for k-quasiclass A operators.