On a class of lambda-hyponormal operators

Abstract

In this paper we define $\hat{I}»$-hyponormal operators on an infinite dimensional Hilbert space $\mathcal{H}$ and find a class of $\hat{I}»$-hyponormal operators that can not be hypercyclic. Also, we study closedness of range and $\hat{I}»$-hyponormality of weighted composition operators on the Hilbert space $\mathcal{H}=L^2(\hat{I}¼)$. Moreover, we apply the hypercyclicity results to $\hat{I}»$-hyponormal weighted composition operators. Finally, we provide some examples to illustrate our main results.

8 pages