Complex symmetric composition operators

Abstract

Let $\phi$ be a linear fractional self-map of the open unit disk $\mathbb{D}$ and $H^2$ the Hardy space of analytic functions on $\mathbb{D}$. The goal of this article is to characterize the linear fractional composition operators $C_{\phi }f=f\circ \phi$ on $H^2$ that are complex symmetric.

The conclusion of Theorem 5.2 is false. The orthogonal decomposition towards the end of the proof is erroneous

References in corpus (1)

• Complex symmetric partial isometries

Cited by in corpus (1)

• Complex symmetric weighted composition operators on Dirichlet spaces and Hardy spaces in the unit ball