On the Index of Callias-type Operators.
On the localization of the spectrum for quasi-selfadjoint extensions of a Carleman operator
In the present work, using a formula describing all scalar spectral functions of a Carleman operator of defect indices in the Hilbert space that we obtained in a previous paper, we derive certain results concerning the localization of the spectrum of quasi-selfadjoint extensions of the operator .
On the method of least squares of finding eigenvalues and eigenfunctions of some symmetric operators. II.
On the Normality of the Unbounded Product of Two Normal Operators
Let A and B be two -non necessarily bounded- normal operators. We give new conditions making their product normal. We also generalize a result by Deutsch et al on normal products of matrices.
On the point spectrum of self-adjoint extensions.
On the problem of convergence of a bounded-below sequence of symmetric forms for the Schrödinger operators
On the singular continuous spectrum of self-adjoint extensions.
On the solvability of the Lyapunov equation for nonselfadjoint differential operators of order 2m with nonlocal boundary conditions
This paper is devoted to the solvability of the Lyapunov equation A*U + UA = I, where A is a given nonselfadjoint differential operator of order 2m with nonlocal boundary conditions, A* is its adjoint, I is the identity operator and U is the selfadjoint operator to be found. We assume that the spectra of A* and -A are disjoint. Under this restriction we prove the existence and uniqueness of the solution of the Lyapunov equation in the class of bounded operators.
On the Spectral Kernel of Symmetric Extensions.
On the spectrum of Robin Laplacian in a planar waveguide
We consider the Laplace operator in a planar waveguide, i.e. an infinite two-dimensional straight strip of constant width, with Robin boundary conditions. We study the essential spectrum of the corresponding Laplacian when the boundary coupling function has a limit at infinity. Furthermore, we derive sufficient conditions for the existence of discrete spectrum.
On Woronowicz's approach to the Tomita-Takesaki theory
The Tomita-Takesaki Theory is very complex and can be contemplated from different points of view. In the decade 1970-1980 several approaches to it appeared, each one seeking to attain more transparency. One of them was the paper of S. L. Woronowicz "Operator systems and their application to the Tomita-Takesaki theory" that appeared in 1979. Woronowicz's approach allows a particularly precise insight into the nature of the Tomita-Takesaki Theory and in this paper we present a brief, but fairly detailed...
One-dimensional graph perturbations of selfadjoint relations.
p-Analytic and p-quasi-analytic vectors
For every symmetric operator acting in a Hilbert space, we introduce the families of p-analytic and p-quasi-analytic vectors (p>0), indexed by positive numbers. We prove various properties of these families. We make use of these families to show that certain results guaranteeing essential selfadjointness of an operator with sufficiently large sets of quasi-analytic and Stieltjes vectors are optimal.
Perturbation of the spectrum οf an essentially selfadjoint operator
The aim of this paper is to find estimates of the Hausdorff distance between the spectra of two nonselfadjoint operators. The operators considered are assumed to have their imaginary parts in some normed ideal of compact operators. In the case of the classical Schatten ideals the estimates are given explicitly.
Perturbations of Selfadjoint Operators with Point Spectra by Restrictions and Selfadjoint Extensions.
Polinomios ortogonales asociados con problemas espectrales
Positive self-adjoint extensions of operators affiliated with a von Neumann algebra.
Positive Selfadjoint Extensions of Positive Symmetric Subspace.
Prolongements maximaux positifs d'opérateurs positifs et problèmes de perturbations singulières
q-deformed circularity for an unbounded operator in Hilbert space
The notion of strong circularity for an unbounded operator is introduced and studied. Moreover, q-deformed circularity as a q-analogue of circularity is characterized in terms of the partially isometric and the positive parts of the polar decomposition.