, Volume 24, Issue 4, pp 497-501

Some generalized theorems onp-hyponormal operators

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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 \(\tilde T = |T|^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0em} 2}} U|T|^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0em} 2}} \) . 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].