Pluricapacity and approximation numbers of composition operators

Daniel Li (1) , Hervé Queffélec (2) , Luis Rodríguez-Piazza

1 LML - Laboratoire de Mathématiques de Lens
2 LPP - Laboratoire Paul Painlevé - UMR 8524

For suitable bounded hyperconvex sets $\Omega$ in $\C^N$, in particular the ball or the polydisk, we give estimates for the approximation numbers of composition operators $C_\phi \colon H^2 (\Omega) \to H^2 (\Omega)$ when $\phi (\Omega)$ is relatively compact in $\Omega$, involving the Monge-Amp\`ere capacity of $\phi (\Omega)$.

Mots clés: approximation numbers; composition operator; Hardy space; hyperconvex domain; Monge-Amp{\`e}re capacity; pluricapacity; pluripotential theory; Zakharyuta conjecture

Domaines: Analyse fonctionnelle [math.FA]

Daniel Li, Hervé Queffélec, Luis Rodríguez-Piazza. Pluricapacity and approximation numbers of composition operators. 2018. ⟨hal-01877752⟩