Now showing items 1-10 of 13
On approximation numbers of composition operators [Article]
We show that the approximation numbers of a compact composition operator on the weighted Bergman spaces Bα of the unit disk can tend to 0 arbitrarily slowly, but that they never tend quickly to 0: they grow at ...
Approximation numbers of composition operators on Hp [Article]
(De Gruyter Open, 2015-01)
We give estimates for the approximation numbers of composition operators on the Hp spaces, 1 ≤ p < ∞.
Compact composition operators on the Dirichlet space and capacity of sets of contact points [Article]
We prove several results about composition operators on the Dirichlet space D⁎. For every compact set K⊆∂D of logarithmic capacity , there exists a Schur function φ both in the disk algebra A(D) and in D⁎ such that the ...
A spectral radius type formula for approximation numbers of composition operators [Article]
For approximation numbers an(Cφ) of composition operators Cφ on weighted analytic Hilbert spaces, including the Hardy, Bergman and Dirichlet cases, with symbol φ of uniform norm <1, we prove that limn→∞[an(Cφ)]1/n=e−1 ...
Some revisited results about composition operators on Hardy spaces [Article]
(European Mathematical Society, 2012)
We generalize, on one hand, some results known for composition operators on Hardy spaces to the case of Hardy-Orlicz spaces HΨ: construction of a “slow” Blaschke product giving a non-compact composition operator on ...
Some examples of compact composition operators on H2 [Article]
We construct, in an essentially explicit way, various composition operators on H2 and study their compactness or their membership in the Schatten classes. We construct: non-compact composition operators on H2 whose symbols ...
Some new properties of composition operators associated with lens maps [Article]
We give examples of results on composition operators connected with lens maps. The first two concern the approximation numbers of those operators acting on the usual Hardy space H2. The last ones are connected with ...
Nevanlinna counting function and Carleson function of analytic maps [Article]
We show that the maximal Nevanlinna counting function and the Carleson function of analytic self-maps of the unit disk are equivalent, up to constants.
Compact composition operators on Hardy-Orlicz and Bergman-Orlicz spaces [Article]
We construct an analytic self-map ϕ of the unit disk and an Orlicz function Ψ for which the composition operator of symbol ϕ is compact on the Hardy-Orlicz space HΨ, but not on the Bergman-Orlicz space BΨ. For that, we first ...
Two results on composition operators on the Dirichlet space [Article]
We show that the decay of approximation numbers of compact composition operators on the Dirichlet space D can be as slow as we wish. We also prove the optimality of a result of O. El-Fallah, K. Kellay, M. Shabankhah ...