Geodesic
Interpolation d'opérateurs entre espaces de fonctions holomorphes
Annales Polonici Mathematici, Tome 56 (1991) no. 1, pp. 97-102 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Let $K$ be a compact subset of an hyperconvex open set $D ⊂ ℂ^n$, 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 $H(D_α)$ is a continuous linear map of $H(D_α)$ into $H(D_α)$, ∀α ∈ ]0,1[ where $D_α = {z ∈ D : ω(z,D,K) α}$.
DOI : 10.4064/ap-56-1-97-102
Mots-clés : interpolation of operators, spaces of analytic functions, common Schauder bases

Patrice Lassere 1

1 
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Patrice Lassere. Interpolation d'opérateurs entre espaces de fonctions holomorphes. Annales Polonici Mathematici, Tome 56 (1991) no. 1, pp. 97-102. doi: 10.4064/ap-56-1-97-102

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