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1
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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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Composition operators on W 1 X are necessarily induced by quasiconformal mappings

100%
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.
3
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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.
4
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Hermitian composition operators on Hardy-Smirnov spaces

100%
Gunatillake G.
Concrete Operators
|
2017
|
tom 4
|
nr 1
7-17
EN
Let Ω be an open simply connected proper subset of the complex plane and φ an analytic self map of Ω. If f is in the Hardy-Smirnov space defined on Ω, then the operator that takes f to f ⃘ φ is a composition operator. We show that for any Ω, analytic self maps that induce bounded Hermitian composition operators are of the form Φ(w) = aw + b where a is a real number. For ceratin Ω, we completely describe values of a and b that induce bounded Hermitian composition operators.
5
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Invertible and normal composition operators on the Hilbert Hardy space of a half–plane

100%
Matache V.
Concrete Operators
|
2016
|
tom 3
|
nr 1
77-84
EN
Operators on function spaces of form Cɸf = f ∘ ɸ, where ɸ is a fixed map are called composition operators with symbol ɸ. We study such operators acting on the Hilbert Hardy space over the right half-plane and characterize the situations when they are invertible, Fredholm, unitary, and Hermitian. We determine the normal composition operators with inner, respectively with Möbius symbol. In select cases, we calculate their spectra, essential spectra, and numerical ranges.
6
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An overview of some recent developments on the Invariant Subspace Problem

75%
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.
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