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Stability of Fredholm properties on interpolation scales. (English) Zbl 0753.46036

Après avoir mis en évidence une propriété caractérisant les opérateurs de Fredholm, les auteurs montrent que si un opérateur \(T\) linéaire de \(A_ 1+A_ 2\) dans \(B_ 1+B_ 2\) est de Fredholm dans un espace d’interpolation \((A_ 1,A_ 2)_ \theta\) dans \((B_ 1,B_ 2)_ \theta\) (ou intérpolation réelle) alors il reste de Fredholm dans des intérpolés dont les paramètres restent dans un voisinage de \(\theta\).

MSC:

46M35 Abstract interpolation of topological vector spaces
47A53 (Semi-) Fredholm operators; index theories
46B70 Interpolation between normed linear spaces
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References:

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