Representation and normality of $$*$$-paranormal absolutely norm attaining operators

Abstract

In this article, we give a representation of absolutely norm attaining $$*$$ -paranormal operators. More specifically, we prove that every $$*$$ -paranormal absolutely norm attaining operator T can be decomposed as $$U\oplus D$$ , where U is a direct sum of scalar multiples of unitary operators and D is an upper triangular block operator matrix. Later, we provide a sufficient condition under which a $$*$$ -paranormal absolutely norm attaining operator is normal.