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Compactness of a difference of composition operators on Dirichlet space

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DMV-PTM Mathematical Meeting 17–20.09.2014, Pozna´n

Compactness of a difference of composition operators on Dirichlet space

Ma lgorzata Michalska

Maria Curie-Sk lodowska University, Lublin, Poland malgorzata.michalska@poczta.umcs.lublin.pl

The talk is based on the joint work with Andrzej M. Michalski Session: Spaces of analytic functions

Let ϕ be a self-map of the unit disk and let Cϕ denote the composition operator with symbol ϕ. We study compactness of the difference Cϕ− Cψ of two composition operators acting on the standard Dirichlet space D and give a necessary condition in the case when ϕ and ψ are finitely valent. We also consider the special case when ϕ and ψ are linear-fractional self-maps.

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