Generalizations of the results on powers of -hyponormal operators - Ito Masatoshi (Journal of Inequalities and Applications, 2001)
Recently, as a nice application of Furuta inequality, Aluthge and Wang (J. Inequal. Appl., 3 (1999), 279–284) showed that "if is a -hyponormal operator for , then is -hyponormal for any positive integer ," and Furuta and Yanagida (Scientiae Mathematicae, to appear) proved the more precise result on powers of -hyponormal operators for . In this paper, more generally, by using Furuta inequality repeatedly, we shall show that "if is a -hyponormal operator for , then is -hyponormal for any positive integer " and a generalization of the results by Furuta and Yanagida in (Scientiae Mathematicae, to appear) on powers of -hyponormal operators for .