Related papers: A Collection of Problems on Spectrally Bounded Ope…
This is an expository-survey on weak stability of bounded linear operators acting on normed spaces in general and, in particular, on Hilbert spaces. The paper gives a comprehensive account of the problem of weak operator stability,…
Algebraic framework for construction of a commuting set of operators that can be interpreted as integrals of motion of the open spin chain with boundary conditions and nearest neighbour interaction is investigated.
We present a new and simple approach to the theory of multiple operator integrals that applies to unbounded operators affiliated with general von Neumann algebras. For semifinite von Neumann algebras we give applications to the Fr\'echet…
In this article we consider 2-dimensional surfaces. We define some new operators which enable us to evaluate quantities of the surface, such invariants, in a more systematic way.
This text is a survey of recent results obtained by the author and collaborators on different problems for non-self-adjoint operators. The topics are: Kramers-Fokker-Planck type operators, spectral asymptotics in two dimensions and Weyl…
In this paper, we introduce the notion of a characteristic operator for closable linear operators and explore their connected spectral properties via equivalence. Additionally, we develop an explicit scheme for constructing characteristic…
There is a connection between *-representations of algebras associated with graphs and the problem about the spectrum of a sum of Hermitian operators (spectral problem). For algebras associated with extended Dynkin graphs we give an…
The present work aims at obtaining estimates for transformation operators for one-dimensional perturbed radial Schr\"odinger operators. It provides more details and suitable extensions to already existing results, that are needed in other…
We introduce a class of (tuples of commuting) unbounded operators on a Banach space, admitting smooth functional calculi, that contains all operators of Helffer-Sj\"ostrand type and is closed under the action of smooth proper mappings.…
Investigation on open questions about perturbation of Hermitian sequences and their spectral symbols. Results on normal sequences are also furnished.
Generalized spectra of differential operators can be related to spectra of preconditioned discretized operators. Obtaining (estimates of) the eigenvalues of the preconditioned discretized operators may lead to better estimating of the…
In the first section we provide a solution to the M. G. Krein problem about an inner description of the space $L_2(\Sigma,H).$ In the second section we introduce the multiplicity function for an operator measure. Making use of the…
We introduce compactness classes of Hilbert space operators by grouping together all operators for which the associated singular values decay at a certain speed and establish upper bounds for the norm of the resolvent of operators belonging…
Complementable operators extend classical matrix decompositions, such as the Schur complement, to the setting of infinite-dimensional Hilbert spaces, thereby broadening their applicability in various mathematical and physical contexts. This…
We study semilinear problems in bounded $C^{1,1}$ domains for non-local operators with a boundary condition. The operators cover and extend the case of the spectral fractional Laplacian. We also study harmonic functions with respect to the…
In [9] a question is raised: if a power bounded operator is quasisimilar to a singular unitary operator, is it similar to this unitary operator? For polynomially bounded operators, a positive answer to this question is known [1], [13]. In…
We introduce a new concept of unbounded solutions to the operator Riccati equation $A_1 X - X A_0 - X V X + V^\ast = 0$ and give a complete description of its solutions associated with the spectral graph subspaces of the block operator…
This note deals with the direct and inverse spectral analysis for a class of infinite band symmetric matrices. This class corresponds to operators arising from difference quations with usual and inner boundary conditions. We give a…
This article gives a fundamental discussion on variable coefficients, self-adjoint, formally partially hypoelliptic differential operators. A generalization of the results to pseudo differential operators, is given in a following article in…
We introduce a notion of $(S+N)$-triangular operators in the Hilbert space using some basic ideas from triangular representation theory. Our notion generalizes the well-known notion of the spectral operators so that many properties of the…