An operator transform from class A to the class of hyponormal operators and its application. (English) Zbl 1098.47006
An operator is said to belong to class \(A\) if \(| T^2| \geq| T| ^2\). In the present paper, the authors give a new operator transform \(\widehat T\) of \(T\) from class \(A\) to the class of hyponormal operators with modulus \(| \widehat T| =| T^2| ^{\frac{1}{2}}\) and show that the spectrum of \(| \widehat T| \) coincides with the one of \(T\) in the case when \(T\) belongs to class \(A\). Moreover, the hyponormality of \(\widehat T\) permits them to obtain some additional properties of class \(A\) operators.
Reviewer: Yufeng Lu (Dalian)