A note on closed *-paranormal operators\\ and Weyl's theorem

Abstract

In this  note we generalize the definition of *-paranormal operator to the case of unbounded operators. We show that every closed symmetric operator as well as every closed hyponormal operator is a closed *-paranormal operator.  Later we discuss a few spectral properties of this class and show that every $\ast$-paranormal operator satisfy the Weyl's theorem. We also prove that the Riesz  idempotent corresponding to an isolated eigenvalue of a $\ast$-paranormal operator is self-adjoint.