Inequalities for the eigenvalues of non-selfadjoint Jacobi operators

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

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.

Error bounds in approximating n-time differentiable functions of self-adjoint operators in Hilbert spaces via a Taylor's type expansion

On utilizing the spectral representation of selfadjoint operators in Hilbert spaces, some error bounds in approximating $n$-time differentiable functions of selfadjoint operators in Hilbert Spaces via a Taylor's type expansion are given.

The spectral properties of differential operators with matrix coefficients on elliptic systems with boundary conditions

Let $$(Lv)(t)=sum^{n} _{i,j=1} (-1)^{j} d_{j} left( s^{2alpha}(t) b_{ij}(t) mu(t) d_{i}v(t)right),$$ be a non-selfadjoint differential operator on the Hilbert space $L_{2}(Omega)$ with Dirichlet-type boundary conditions. In continuing of papers [10-12], let the conditions made on the operator $ L$ be sufficiently more general than [11] and [12] as defined in Section $1$. In this paper, we estim...

The Horn Conjecture for Sums of Compact Selfadjoint Operators

We determine the possible nonzero eigenvalues of compact selfadjoint operators A, B(1), B(2), . . ., B(m) with the property that A = B(1) +B(2) +· · ·+B(m). When all these operators are positive, the eigenvalues were known to be subject to certain inequalities which extend Horn’s inequalities from the finite-dimensional case when m = 2. We find the proper extension of the Horn inequalities and ...