Various theorems on lifting strong commutants of unbounded sub-normal (as well as formally subnormal) operators are proved. It is shown that the strong symmetric commutant of a closed symmetric operator S lifts to the strong commutant of some tight selfadjoint extension of S. Strong symmetric commutants of orthogonal sums of subnormal operators are investigated. Examples of (unbounded) irreduci...

We construct efficient approximations for the eigenfunctions of non-selfadjoint Schrödinger operators in one dimension. The same ideas also apply to the study of resonances of self-adjoint Schrödinger operators which have dilation analytic potentials. In spite of the fact that such eigenfunctions can have surprisingly complicated structures with multiple local maxima, we show that a suitable ad...

A convergent iterative process is constructed for solving any solvable linear equation in a Hilbert space, including equations with unbounded, closed, densely defined linear operators. The method is proved to be stable towards small perturbation of the data. Some abstract results are established and used in an analysis of variational regularization method for equations with unbounded linear ope...

The aim of this paper is to investigate spectral properties of second order elliptic operators with measurable coefficients. Namely, we study the problems of L-independence of the spectrum and stability of the essential spectrum. The problem of L-independence of the spectrum for elliptic operators has a long history going back to B. Simon [30] where the question was posed for Schrödinger operat...

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...

We define and study the noncommutative spectral flow for paths of regular selfadjoint Fredholm operators on a Hilbert C∗-module. We give an axiomatic description and discuss some applications. One of them is the definition a noncommutative Maslov index for paths of Lagrangians which appears in a splitting formula for the spectral flow. Analogously we study the spectral flow for odd operators on...