Differences of composition operators on the space of bounded analytic functions in the polydisc (Q1008558)

Summary: This paper gives some estimates of the essential norm for the difference of composition operators induced by \(\varphi \) and \(\psi \) acting on the space \(H^{\infty }(D^{n})\) of bounded analytic functions on the unit polydisc \(D^{n}\), where \(\varphi \) and \(\psi \) are holomorphic self-maps of \(D^{n}\). As a consequence, one obtains conditions in terms of the Carathéodory distance on \(D^{n}\) that characterizes those pairs of holomorphic self-maps of the polydisc for which the difference of two composition operators on \(H^{\infty }(D^{n})\) is compact.