Limit Properties of Eigenvalues in Spectral Gaps

Let S be a closed symmetric operator or relation with defect numbers (1, 1). The selfadjoint extensions A(τ) of S are parametrized over τ ∈ ℝ∪{∞}. When the selfadjoint extension A(0) has a spectral gap (α, β), then the same is true for all the other selfadjoint extensions A(τ) of S with the possible exception of an isolated eigenvalue λ(τ) of A(τ). The limiting properties of this isolated eigenvalue are studied in terms of τ .