Necessary condition for compactness of a difference of composition operators on the Dirichlet space
Michalska, Małgorzata · Michalski, Andrzej
Original · EN
Let φ be a self-map of the unit disk and let Cφ denote the composition operator acting on the standard Dirichlet space D. A necessary condition for compactness of a difference of two bounded composition operators acting on D, is given. As an application, a characterization of disk automorphisms φ and ψ for which the commutator [C*ψ,Cφ] is compact, is given.
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