Antinormal Weighted Composition Operators

Abstract

Let $l^{\mathrm{2}}=L^{\mathrm{2}}\left(\mathbb{N},\mu \right)$, where $\mathbb{N}$ is set of all positive integers and $\mu$ is the counting measure whose $\sigma$-algebra is the power set of $\mathbb{N}$. In this paper, we obtain necessary and sufficient conditions for a weighted composition operator to be antinormal on the Hilbert space $l^{\mathrm{2}}$. We also determine a class of antinormal weighted composition operators on Hardy space $H^{\mathrm{2}}\left(\mathbb{D}\right)$.