Journal of Inequalities and Applications
Volume 6 (2001), Issue 1, Pages 1-15

Generalizations of the results on powers of p-hyponormal operators

Masatoshi Ito

Department of Applied Mathematics, Faculty of Science, Science University of Tokyo, 1-3 Kagurazaka, Shinjuku, Tokyo 162-8601, Japan

Received 31 August 1999; Revised 10 September 1999

Copyright © 2001 Masatoshi Ito. 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.


Recently, as a nice application of Furuta inequality, Aluthge and Wang (J. Inequal. Appl., 3 (1999), 279–284) showed that “ifT is a p-hyponormal operator forp(0,1], thenTnisp/n-hyponormal for any positive integern,” and Furuta and Yanagida (Scientiae Mathematicae, to appear) proved the more precise result on powers of p-hyponormal operators for p(0,1]. In this paper, more generally, by using Furuta inequality repeatedly, we shall show that “ifT is a p-hyponormal operator forp>0, thenTnismin{1,p/n}-hyponormal for any positive integern” and a generalization of the results by Furuta and Yanagida in (Scientiae Mathematicae, to appear) on powers of p-hyponormal operators for p>0.