A theory of non-unitary unbounded similarity transformation operators is developed. To this end the class of J-unitary operators U is introduced. These operators are similar to unitary operators in their algebraic aspects but differ in their topological properties. It is shown how J-unitary operators are related to so-called J-biorthonormal systems and J-selfadjoint projections. Families {Uα} o...

The aim of this note is to study the submajorization inequalities for $tau$-measurable operators in a semi-finite von Neumann algebra on a Hilbert space with a normal faithful semi-finite trace $tau$. The submajorization inequalities generalize some results due to Zhang, Furuichi and Lin, etc..

We study the structure of the Fuč́ık spectra for the linear multipoint differential operators. We introduce a variational approach in order to obtain a robust and global algorithm which is suitable for the exploration of unknown Fuč́ık spectrum structure. We apply our approach in the case of the four-point selfadjoint differential operator of the fourth order which is closely connected to the non...

Spectral points of positive and negative type, and type π+ and type π− for closed linear operators and relations in Krein spaces are introduced with the help of approximative eigensequences. The main objective of the paper is to study these sign type properties in the non-selfadjoint case under various kinds of perturbations, e.g. compact perturbations and perturbations small in the gap metric....

Let P be a selfadjoint elliptic operator of order m > 0 acting on the sections of a Hermitian vector bundle over a compact Riemannian manifold of dimension n. General arguments show that its zeta and eta functions may have poles only at points of the form s = k m , where k ranges over all non-zero integers ≤ n. In this paper, we construct elementary and explicit examples of perturbations of P w...