Eigenvalue asymptotics for randomly perturbed non-selfadjoint operators

Spectral perturbation bounds for selfadjoint operators I∗

We give general spectral and eigenvalue perturbation bounds for a selfadjoint operator perturbed in the sense of the pseudo-Friedrichs extension. We also give several generalisations of the aforementioned extension. The spectral bounds for finite eigenvalues are obtained by using analyticity and monotonicity properties (rather than variational principles) and they are general enough to include ...

Non-self-adjoint Differential Operators

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...

On the Spectral Properties of Degenerate Non-selfadjoint Elliptic systems of Differential Operators

Inequalities for the eigenvalues of non-selfadjoint Jacobi operators

We prove Lieb-Thirring-type bounds on eigenvalues of non-selfadjoint Jacobi operators, which are nearly as strong as those proven previously for the case of selfadjoint operators by Hundertmark and Simon. We use a method based on determinants of operators and on complex function theory, extending and sharpening earlier work of Borichev, Golinskii and Kupin.

Mathematik-Bericht 2010/5 An eigenvalue estimate and its application to non-selfadjoint Jacobi and Schrödinger operators

For bounded linear operators A,B on a Hilbert space H we show the validity of the estimate ∑ λ∈σd(B) dist(λ,Num(A)) ≤ ‖B −A‖pSp , p ≥ 1, and apply it to recover and improve some Lieb-Thirring type inequalities for non-selfadjoint Jacobi and Schrödinger operators.