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Compact differences of composition operators on weighted Dirichlet spaces

100%
Allen R., Heller K., Pons M.
Open Mathematics
|
2014
|
tom 12
|
nr 7
1040-1051
EN
Here we consider when the difference of two composition operators is compact on the weighted Dirichlet spaces . Specifically we study differences of composition operators on the Dirichlet space and S 2, the space of analytic functions whose first derivative is in H 2, and then use Calderón’s complex interpolation to extend the results to the general weighted Dirichlet spaces. As a corollary we consider composition operators induced by linear fractional self-maps of the disk.
2
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Bloch-to-Hardy composition operators

100%
Doubtsov E., Petrov A.
Open Mathematics
|
2013
|
tom 11
|
nr 6
985-1003
EN
Let φ be a holomorphic mapping between complex unit balls. We characterize those regular φ for which the composition operators C φ: f ↦ f ○ φ map the Bloch space into the Hardy space.
3
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An overview of some recent developments on the Invariant Subspace Problem

84%
Chalendar I., Partington J. R.
Concrete Operators
|
2013
|
tom 1
1-10
EN
This paper presents an account of some recent approaches to the Invariant Subspace Problem. It contains a brief historical account of the problem, and some more detailed discussions of specific topics, namely, universal operators, the Bishop operators, and Read’s Banach space counter-example involving a finitely strictly singular operator.
4
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Composition operators on W 1 X are necessarily induced by quasiconformal mappings

84%
Kleprlík L.
Open Mathematics
|
2014
|
tom 12
|
nr 8
1229-1238
EN
Let Ω ⊂ ℝn be an open set and X(Ω) be any rearrangement invariant function space close to L q(Ω), i.e. X has the q-scaling property. We prove that each homeomorphism f which induces the composition operator u ↦ u ℴ f from W 1 X to W 1 X is necessarily a q-quasiconformal mapping. We also give some new results for the sufficiency of this condition for the composition operator.
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