Adjoints of linear fractional composition operators on weighted Hardy spaces

Abstract

It is well known that on the Hardy space $H^2(\mathbb{D})$ or weighted Bergman space $A_{\alpha }^2(\mathbb{D})$ over the unit disk, the adjoint of a linear fractional composition operator equals the product of a composition operator and two Toeplitz operators. On $S^2(\mathbb{D})$, the space of analytic functions on the disk whose first derivatives belong to $H^2(\mathbb{D})$, Heller showed that a similar formula holds modulo the ideal of compact operators. In this paper we investigate what the situation is like on other weighted Hardy spaces.

arXiv comment10 pages, accepted for publication in Acta Sci. Math. (Szeged)

References in corpus (1)

• Adjoints of composition operators with rational symbol