  In this paper, we investigate the spectral radius al- gebras related to the
weighted conditional expectation operators on the Hilbert spaces L2(F). We give
a large classes of operators on L2(F) that have the same spectral radius
algebra. As a con- sequence 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 condi- tional expectation operator on L2(F) or a rank one
operator on the arbitrary Hilbert space H.
