Abstract. 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 $\lambda_o \in\bf C$, in the case that $T$ admits a generalized Kato decomposition property.

AMS Subject Classification (1991): 47A53, 47A55

Keyword(s): Single valued extension property, Fredholm theory

Received July 6, 2000, and in final form October 2, 2000. (Registered under 2818/2009.)