A note on the punctured neighbourhood theorem

Abstract

The punctured neighbourhood theorem an be interpreted as saying that if 0 ∈ C is on the boundary of the spectrum of a Fredholm operator then it must be an isolated point of that spectrum. This extends to semi-Fredholm operators, in particular to operators with closed range and finite dimensional null space. In this note we generalise both the finite dimensionality of the null space and the scalars involved in the definition of an isolated point of the spectrum.