Paranormal weighted conditional type operators

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.