Journal of Inequalities and Applications
Volume 5 (2000), Issue 4, Pages 367-380
On powers of -hyponormal and log-hyponormal operators
Department of Applied Mathematics, Faculty of Science, Science University of Tokyo, 1-3 Kagurazaka, Shinjuku, Tokyo 162-8601, Japan
Received 17 May 1999; Revised 14 July 1999
Copyright © 2000 Takayuki Furuta and Masahiro Yanagida. 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.
A bounded linear operator on a Hilbert space is said to be -hyponormal for if , and is said to be log-hyponormal if is invertible and . Firstly, we shall show the following extension of our previous result: If is -hyponormal for , then and hold for all positive integer . Secondly, we shall discuss the best possibilities of the following parallel result for log-hypponormal operators by Yamazaki: If is log-hyponormal, then and hold for all positive integer .