Interpolation d'opérateurs entre espaces de fonctions holomorphes

Patrice Lassere¹

¹

Annales Polonici Mathematici, Tome 56 (1991) no. 1, pp. 97-102.

Résumé

Let $K$ be a compact subset of an hyperconvex open set $D\subset {ℂ}^n$, forming with D a Runge pair and such that the extremal p.s.h. function ω(·,K,D) is continuous. Let H(D) and H(K) be the spaces of holomorphic functions respectively on D and K equipped with their usual topologies. The main result of this paper contains as a particular case the following statement: if T is a continuous linear map of H(K) into H(K) whose restriction to H(D) is continuous into H(D), then the restriction of T to $H(D_{\alpha })$ is a continuous linear map of $H(D_{\alpha })$ into $H(D_{\alpha })$, ∀α ∈ ]0,1[ where $D_{\alpha }=z\in D:\omega (z,D,K)\alpha$.

Détail

DOI : 10.4064/ap-56-1-97-102

Mots-clés : interpolation of operators, spaces of analytic functions, common Schauder bases