Related papers: Residual Spectrum of Power Bounded Operators

We discuss several open problems on spectrally bounded operators, some new, some old, adding in a few new insights.

The paper investigates the variation of the spectrum of operators in infinite dimensional Banach spaces. In particular, it is shown that the spectrum function is Borel from the space of bounded operators on a separable Banach space;…

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…

The relative distance between eigenvalues of the compression of a not necessarily semibounded self-adjoint operator to a closed subspace and some of the eigenvalues of the original operator in a gap of the essential spectrum is considered.…

Ordinary and partial differential operators with an indefinite weight function can be viewed as bounded perturbations of non-negative operators in Krein spaces. Under the assumption that 0 and $\infty$ are not singular critical points of…

This paper provides a description of the spectrum of diagonal perturbation of weighted shift operator acting on a separable Hilbert space.

We study the spectrum of a periodic self-adjoint operator on the axis perturbed by a small localized nonself-adjoint operator. It is shown that the continuous spectrum is independent of the perturbation, the residual spectrum is empty, and…

Starting from the classic definitions of local resolvent set and spectrum of a linear bounded operator on a Banach space, we introduce the local resolvent set and spectrum, the local space and the single-valued extention property of a…

In this note we provide an explicit lower bound on the spectral gap of one-dimensional Schr\"odinger operators with non-negative bounded potentials and subject to Neumann boundary conditions.

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.

Important spectral features, such as the emptiness of the residual spectrum, countability of the point spectrum, provided the space is separable, and a characterization of spectral gap at $0$, known to hold for bounded scalar type spectral…

We provide a description of the spectrum and essential spectra of invertible weighted composition operators acting in some algebras of smooth functions on the interval.

Let $T$ denote a positive operator with spectral radius $1$ on, say, an $L^p$-space. A classical result in infinite dimensional Perron--Frobenius theory says that, if $T$ is irreducible and power bounded, then its peripheral point spectrum…

We furnish a simple way of constructing an unbounded closed linear operator in a complex Banach space, whose spectrum is an arbitrary nonempty closed, in particular compact, subset of the complex plane.

In this paper, we describe the spectrum properties of mixed operators, precisely the superposition of the classical Laplace operator and the fractional Laplace operator in the presence of mixed boundary conditions, that is \begin{equation}…

A bounded operator $u$ on $X$ is called rigid when there is an increasing sequence of positive integers $(n_k)_{k\geq 1}$, such that for every $x$ in $X$ we have $\lim_{k \rightarrow +\infty} u^{n_k} x = x$. For any $r$ in $[0,1]$, we…

Spectrum of the volume integral operator of the three-dimensional electromagnetic scattering is analyzed. The operator has both continuous essential spectrum, which dominates at lower frequencies, and discrete eigenvalues, which spread out…

Some elementary inequalities providing upper bounds for the difference of the norm and the numerical radius of a bounded linear operator on Hilbert spaces under appropriate conditions are given.

Each bounded operator T on an infinite dimensional Hilbert space H is a sum of three operators that are similar to positive operators; two such operators are sufficient if T is not a compact perturbation of a scalar. The spectra of L\"uders…

In this note, we introduce and study the left (right) pseudospectrum and left (right) condition pseudospectrum of bounded linear operators on ultrametric Banach spaces. We prove some results about them.