Complex symmetric weighted composition operators on weighted Hardy space

In this paper various conditions under which a weighted composition operator $W_{\psi,\phi}$ on the weighted Hardy space $H^2(\beta)$ becomes complex symmetric with respect to some special conjugation have been explored. We also investigate some important properties of the complex symmetric operator $W_{\psi,\phi}$ such as hermiticity and isometry.

In this paper various conditions under which a weighted composition operator $W_{\psi,\phi}$ on the weighted Hardy space $H^2(\beta)$ becomes complex symmetric with respect to some special conjugation have been explored. We also investigate some important properties of the complex symmetric operator $W_{\psi,\phi}$ such as hermiticity and isometry.

Composition operator Complex symmetric Weighted Hardy space Conjugation

Composition operator Complex symmetric Weighted Hardy space Conjugation