Abstract. It is well known that on the Hardy space $H^2(\mathbb{D})$ or weighted Bergman space $A^2_{\alpha }(\mathbb{D})$ 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.

DOI: 10.14232/actasm-015-801-z

AMS Subject Classification (1991): 47B33

Keyword(s): composition operator, adjoint, weighted Hardy space

Received July 3, 2015, and in revised form August 31, 2015. (Registered under 51/2015.)