Single-valued extension property at the points of the approximate point spectrum.
Let \(X\) be a complex Banach space. A linear bounded operator \(T\) on this space is said to have the single-valued extension property at the point \(\lambda_{0}\), if for every open disc \(D\) centered at \(\lambda_{0}\) the only analytic function \(f:D\rightarrow X\) which satisfies the equation \((\lambda I-T)f(\lambda)=0\) for all \(\lambda\in D\) is the function \(f\equiv 0\). The authors in the present paper obtain necessary and sufficient conditions for this property for operators from some special class. As a corollary of these results, they deduce several results on cluster points of some distinguished parts of the spectrum.
scientific article; zbMATH DE number 1915741