Some Classes of Absolutely Norm Attaining Weighted Shift operators on Directed Graphs

Abstract

In this paper we study absolutely norm attaining quasi-$\ast$-paranormal weighted shifts on directed graphs and give some examples. Moreover we give some examples which show that the spectrum of a positive absolutely norm attaining operator containing more than one eigenvalue with infinite multiplicity. Later we investigate weighted composition and Lambert operators on directed graphs.

Revised version. Substantial Revision made.16 pages