Linear isometries of some function algebras

Abstract

Linear isometries of a class of logmodular algebras which are generated by unitary functions are represented by Holszty\'{n}ski type weighted composition operators. The description of these operators leads - among other things - to a characterization of the linear isometries of the disc algebra and of the Hardy space of all bounded holomorphic functions on the open unit disc of $\mathbb{C}$. Spectral properties of these isometries are also investigated.