Paranormal weighted conditional type operators

TL;DR

This paper investigates various subclasses of paranormal weighted conditional expectation operators on L^2 spaces, analyzing their spectral properties and introducing new classifications within this operator framework.

Contribution

It introduces and studies new subclasses of paranormal weighted conditional expectation operators, expanding understanding of their spectral characteristics.

Findings

Characterization of spectra for these operators

Identification of conditions for different paranormal subclasses

Analysis of spectral properties and their implications

Abstract

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.