Some Inequalities On Powers Of P-hyponormal Operators

In this paper, H means a complex Hilbert space. A bound(?)d linear operator T on H is said to be positive (in symbol: T≥0) if (Tx, x)≥0 for any x∈H. Also an operator T is said to be strictly positive (in symbol: T > 0) if T is positive and invertiblc.In this paper, we shall study some inequalities on powers of p-hyponormal operators, showing the further extensions of the results of T. Furuta, M. Yanagida and T. Ya-mazaki;At the same time, we discuss the best possibility of our results.Secondly, we study log-hyponormal operators and chaotic order. We give out the results of log-hyponormal operators which are parallel to the results of p-hyponormal operators; we also discuss the best possibility of our results.