SPECTRAL RADIUS ALGEBRAS OF WCE OPERATORS

In this paper, we investigate the spectral radius algebras related to the weighted conditional expectation operators on the Hilbert spaces L-2(F). We give a large classes of operators on L-2(F) that have the same spectral radius algebra. As a consequence we get that the spectral radius algebras of a weighted conditional expectation operator and its Aluthge transformation are equal. Also, we obtain an ideal of the spectral radius algebra related to the rank one operators on the Hilbert space H. Finally we get that the operator T majorizes all closed range elements of the spectral radius algebra of T, when T is a weighted conditional expectation operator on L-2(F) or a rank one operator on the arbitrary Hilbert space H.