On totally *-paranormal operators

Abstract

In this paper we study some properties of a totally*-paranormal operator (defined below) on Hilbert space. In particular, we characterize a totally*-paranormal operator. Also we show that Weyl's theorem and the spectral mapping theorem hold for totally*-paranormal operators through the local spectral theory. Finally, we show that every totally*-paranormal operator satisfies an analogue of the single valued extension property for W 2(D, H) and some of totally*-paranormal operators have scalar extensions. © Mathematical Institute, Academy of Sciences of Czech Republic 2006.