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Stability of semi-Fredholm properties in complex interpolation spaces. (English) Zbl 1241.47010

Let \(\overrightarrow{E}\) and \(\overrightarrow{ F}\) be compatible pairs of Banach spaces. In the present paper, the authors consider the complex interpolation method. Among other results, they show that, if \( \overrightarrow{S}\) is an interpolation morphism between regular couples \(\overrightarrow{E}\) and \(\overrightarrow{F}\) and if \(S_{[\lambda]}\) is semi-Fredholm for some \(\lambda \in (0,1)\), then the nullities and deficiencies are constant in some neighborhood of \(\lambda\). This improves a result of E. Albrecht [Oper. Theory Adv. App. 14, 13–37 (1984; Zbl 0564.47003)].

MSC:

47A53 (Semi-) Fredholm operators; index theories
46B70 Interpolation between normed linear spaces
47A55 Perturbation theory of linear operators

Citations:

Zbl 0564.47003
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References:

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