Some Properties of Algebraically Paranormal Operator

Zaman Adel  Rashid; Buthainah A.A.  Ahmed

doi:10.24996/ijs.2022.63.8.31

Authors

Zaman Adel Rashid Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq
Buthainah A.A. Ahmed Department of Mathematics, College of Science, University of Baghdad, Baghdad, Iraq

DOI:

https://doi.org/10.24996/ijs.2022.63.8.31

Keywords:

Weyl's Theorem, Algebraically paranormal operator, Polaroid Operator

Abstract

Through this study, the following has been proven, if is an algebraically paranormal operator acting on separable Hilbert space, then satisfies the ( ) property and is also satisfies the ( ) property for all . These results are also achieved for ( ) property.

In addition, we prove that for a polaroid operator with finite ascent then after the property ( ) holds for for all .