  In this paper, some sub-classes of paranormal weighted conditional
expectation type operators, such as *-paranormal, quasi-*-paranormal and (n;
k)-quasi-*-paranormal weighted conditional expectation type opera- tors on
$L^2(\Sigma)$ are investigated. Also, some applications about the spectrum,
point spectrum, joint point spectrum, approximate point spectrum and joint
approximate point spectrum of these classes are presented.
