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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...
L’article donne des réponses optimales ou presque optimales aux questions suivantes, qui remontent à Stieltjes, Landau et Bohr, et concernent des séries de Dirichlet
et leur produit
1. Supposant que les sont convergentes aux points et absolument convergentes aux points en quels points s’ensuit-il que est convergente ?
2. Supposant que les sont convergentes...
give estimates for the approximation numbers of composition operators on the Hp spaces, 1 ≤ p < ∞
We give new proofs that some Banach spaces have Pełczyński's property (V).
We study the canonical injection from the Hardy-Orlicz space into the Bergman-Orlicz space .
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