Some generalized theorems onp-hyponormal operators

Abstract

A bounded linear operatorT is calledp-Hyponormal if (T ^*T)^p≥(TT ^*)^p, 0<p≤1. In Aluthge [1], we studied the properties of p-hyponormal operators using the operator$\tilde T = |T|^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} U|T|^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}}$. In this work we consider a more general operator$T_ \in = |T|^ \in U|T|^{1 - \in } , 0< \in \leqslant 1/2$, and generalize some properties of p-hyponormal operators obtained in [1].