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 ...

We study the canonical injection from the Hardy-Orlicz space HΨ into the Bergman–Orlicz space BΨ..

We give estimates for the approximation numbers of composition operators on the Hp spaces, 1 ≤ p < ∞.

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 ...

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 ...

We prove that, for every α>−1, the pull-back measure φ(Aα) of the measure dAα(z)=(α+1)(1−|z|2)αdA(z), where A is the normalized area measure on the unit disk D, by every analytic self-map φ:D→D is not only an (α+2)-Carleson ...

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 ...

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 ...

We give new proofs that some Banach spaces have Peczynski's property (V)

We study the approximation numbers of weighted composition operators f 7→ w · (f ◦ ϕ) on the Hardy space H2 on the unit disc. For general classes of such operators, upper and lower bounds on their approximation numbers ...