Classes of Operators Associated with (f, g)-Aluthge Transforms

A. Let T B(H) be a bounded linear operator on a Hilbert space H with the polar decomposition, where f and g both are non-negative continuous functions on [0, [ such that f (x)g(x) = x, for all x 0. In this paper, firstly, we investigate the relationship between this transform and several classes of operators as quasi-normal, normal, positive, nilpotent and closed range operators.Secondly, we show that under some conditions the (f, g)-Aluthge transform possesses the polar decomposition.Lastly, we provide a characterization of binormal operators from the viewpoint of the polar decomposition and the (f, g)-Aluthge transform.