We describe the convex set of the eigenvalues of hermitian matrices which are majorized by sum of m hermitian matrices with prescribed eigenvalues. We extend our characterization to selfadjoint nonnegative (definite) compact operators on a separable Hilbert space. We give necessary and sufficient conditions on the eigenvalue sequence of a selfadjoint nonnegative compact operator of trace class ...

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.

We study a few classes of Hilbert space operators whose matrix representations are complex symmetric with respect to a preferred orthonormal basis. The existence of this additional symmetry has notable implications and, in particular, it explains from a unifying point of view some classical results. We explore applications of this symmetry to Jordan canonical models, selfadjoint extensions of s...

Singular boundary conditions are formulated for non-selfadjoint Sturm-Liouville operators with singularities and turning points. For boundary value problems with singular boundary conditions properties of the spectrum are studied and the completeness of the system of root functions is proved.

Distinguished selfadjoint extensions of operators which are not semibounded can be deduced from the positivity of the Schur Complement (as a quadratic form). In practical applications this amounts to proving a Hardy-like inequality. Particular cases are Dirac-Coulomb operators where distinguished selfadjoint extensions are obtained for the optimal range of coupling constants.

In this paper we provide sharp error bounds in approximating the weighted Riemann-Stieltjes integral R b a f (t) g (t) d (t) by the weighted trapezoidal rule f(a)+f(b) 2 R b a g (t) d (t) : Applications for continuous functions of selfadjoint operators in complex Hilbert spaces are given as well.