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The single valued extension property and the generalized Kato decomposition property. (English) Zbl 1017.47008
Summary: This paper concerns the single valued extension property of a bounded operator $$T\in L(X)$$ on a Banach space $$X$$. We shall be mostly interested in a local version of this property, the single valued extension property at a point $$\lambda_0\in \mathbb C$$, in the case that $$T$$ admits a generalized Kato decomposition property.

##### MSC:
 47A53 (Semi-) Fredholm operators; index theories 47A55 Perturbation theory of linear operators
##### Keywords:
extension property; Banach space