Given the symmetric operator AN obtained by restricting the self-adjoint operator A to N , a linear dense set, closed with respect to the graph norm, we determine a convenient boundary triple for the adjoint A N and the corresponding Weyl function. These objects provide us with the self-adjoint extensions of AN and their resolvents.

In 1937, von Neumann [31] gave a famous characterization of unitarily invariant matrix norms (that is, norms f on Cp×q satisfying f(uxv) = f(x) for all unitary matrices u and v and matrices x in Cp×q). His result states that such norms are those functions of the form g ◦ , where the map x ∈ Cp×q 7→ (x) ∈ R has components the singular values 1(x) ≥ 2(x) ≥ · · · ≥ p(x) of x (assuming p ≤ q) and g...

We describe methods which have been used to analyze the spectrum of non-self-adjoint differential operators, emphasizing the differences from the self-adjoint theory. We find that even in cases in which the eigenfunctions can be determined explicitly, they often do not form a basis; this is closely related to a high degree of instability of the eigenvalues under small perturbations of the opera...