Study of non-normal operators in a complex Hilbert space

Abstract

This paper is on some special characteristics of non-normal operators. We first seek to show that if a bounded operator Tis paranormal: what about Tl? Here its enough to find aTE 8(H) for which Tl is not hyponormal but Tis hyponormal. Similarly, we also use this result to prove that if T is paranormal then so is 7". We also show that if T is k-paranormal, then it is normaloid. We discuss a result that gives a sufficient condition for an operator to be k-paranormal using spectral theorem of self-adjoint operators. Lastly in this paper we show that the class of k-hyperparanormal operators is strictly smaller than the class of k-paranormal operators and the strong closure of hypo normal operators is contained in the class of paranormal operators.