Spectral radius algebras of WCE operators

چکیده مقاله

In this paper, we investigate the spectral radius algebras 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 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
L2(F) or a rank one operator on the arbitrary Hilbert space H .