Related papers: On certain spectral features inherent to scalar ty…
Let $\mathcal{B}(H)$ be the bounded, linear operators on a separable Hilbert space equipped with the norm topology. A property is called typical if the set of operators fulfilling the property is co-meager. We show that having non-empty…
General, especially spectral, features of compact normal operators in quaternionic Hilbert spaces are studied and some results are established which generalize well-known properties of compact normal operators in complex Hilbert spaces.…
In this paper, we study one of the fundamental notions in dynamical systems, the shadowing of invertible (bounded and linear) operators on a Hilbert space. Although the problem of finding a spectral characterization for shadowing has been…
We study the spectral properties of bounded and unbounded Jacobi matrices whose entries are bounded operators on a complex Hilbert space. In particular, we formulate conditions assuring that the spectrum of the studied operators is…
In this paper, the spectrum, residual spectrum, point spectrum and spectral radius of weighted conditional type operators are computed. As an application, we give an equivalent condition for weighted conditional type operators to be…
We give a characterisation of the spectral properties of linear differential operators with constant coefficients, acting on functions defined on a bounded interval, and determined by general linear boundary conditions. The boundary…
Partial operators can have void or unbounded spectra. Contrarily to what is written in Dunford-Schwarz, the reason is not in the fact they are unounded operators.
We develop an abstract method to identify spectral points of definite type in the spectrum of the operator $T_1\otimes I_2 + I_1\otimes T_2$. The method is applicable in particular for non-self-adjoint waveguide type operators with…
Spectral singularities are among generic mathematical features of complex scattering potentials. Physically they correspond to scattering states that behave like zero-width resonances. For a simple optical system, we show that a spectral…
We study the typical behavior of bounded linear operators on infinite dimensional complex separable Hilbert spaces in the norm, strong-star, strong, weak polynomial and weak topologies. In particular, we investigate typical spectral…
We consider fractional differentiation operators in various senses and show that the strictly accretive property is the common property of fractional differentiation operators. Also we prove that the sectorial property holds for…
We establish spectral inclusion and mapping theorems for scalar type spectral operators, generalizing their counterparts for normal operators. Thereby, we extend a precise weak spectral mapping theorem, known to hold for $C_0$-semigroups of…
We consider selfadjoint operators obtained by pasting a finite number of boundary relations with one-dimensional boundary space. A typical example of such an operator is the Schr\"odinger operator on a star-graph with a finite number of…
We present a spectral analysis for matrix scaling and operator scaling. We prove that if the input matrix or operator has a spectral gap, then a natural gradient flow has linear convergence. This implies that a simple gradient descent…
We study the spectrum of one dimensional integral operators in bounded real intervals of length $2L$, for value of $L$ large. The integral operators are obtained by linearizing a non local evolution equation for a non conserved order…
The goal of this note is to study the spectrum of a self-adjoint convolution operator in $L^2(\mathbb R^d)$ with an integrable kernel that is perturbed by an essentially bounded real-valued potential tending to zero at infinity. We show…
We compare the spectral properties of two kinds of linear operators characterizing the (classical) geodesic flow and its quantization on connected locally finite graphs without dead ends. The first kind are transfer operators acting on…
Using the notion of spectral flow, we suggest a simple approach to various asymptotic problems involving eigenvalues in the gaps of the essential spectrum of self-adjoint operators. Our approach uses some elements of the spectral shift…
An ordinary differential operator of the fourth order with coefficients converging at infinity sufficiently rapidly to constant limits is considered. Scattering theory for this operator is developed in terms of special solutions of the…
We consider a semi-periodic two-dimensional Schr\"odinger operator which is cut at an angle. When the cut is commensurate with the periodic lattice, the spectrum of the operator has the band-gap Bloch structure. We prove that in the…