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.

arXiv commentRevised version. Substantial Revision made.16 pages