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Composition operators in the Dirichlet series setting

100%

Queffélec H.

Banach Center Publications

2007

tom 75

nr 1

261-287

In this work, we begin with a survey of composition operators on the Hardy space H² and on the Wiener algebra A⁺ of absolutely convergent Taylor series, with special emphasis on their compactness, or invertibility, or isometric character. The main results are due respectively to J. Shapiro and D.~Newman. In a second part, we present more recent results, due to Gordon and Hedenmalm on the one hand, and to Bayart, the author et al. on the other hand, concerning the analogues of H² and A⁺ in the setting of Dirichlet series. We are led to the intermediate study of Taylor series in several, or countably many, variables. We finish with some open problems.

The canonical injection of the Hardy-Orlicz space $H^{Ψ}$ into the Bergman-Orlicz space $𝔅^{Ψ}$

51%

Lefèvre P. , Li D. , Queffélec H. , Rodríguez-Piazza L.

Studia Mathematica

2011

tom 202

nr 2

123-144

We study the canonical injection from the Hardy-Orlicz space $H^{Ψ}$ into the Bergman-Orlicz space $𝔅^{Ψ}$.

Approximation numbers of composition operators on Hp

51%

Li D. , Queffélec H. , Rodríguez-Piazza L.

Concrete Operators

2015

tom 2

nr 1

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

Weak compactness and Orlicz spaces

51%

Lefèvre P. , Li D. , Queffélec H. , Rodríguez-Piazza L.

Colloquium Mathematicum

2008

tom 112

nr 1

23-32

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