Journal of Inequalities and Applications 
Volume 6 (2001), Issue 1, Pages 1-15
doi:10.1155/S1025583401000017

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

Abstract

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.