Related papers: On the Peripheral Spectrum of Positive Operators
We consider the third order operator with small 1-periodic coefficients on the real line. The spectrum of the operator is absolutely continuous and covers all real line. Under the minimal conditions on the coefficients we show that there…
Let H be a separable, infinite dimensional Hilbert space and let S be a countable subset of H. Then most positive operators on H have the property that every nonzero vector in the span of S is cyclic, in the sense that the set of operators…
In this paper we present some spectral property for quotient bounded operators and locally bounded operators on locally convex spaces. We introduce the spectral radius of a quotient bounded operator and we show that the Gelfand formula for…
The first representation theorem establishes a correspondence between positive, self-adjoint operators and closed, positive forms on Hilbert spaces. The aim of this paper is to show that some of the results remain true if the underlying…
We identify concrete examples of hypercyclic generalised derivations acting on separable ideals of operators and establish some necessary conditions for their hypercyclicity. We also consider the dynamics of elementary operators acting on…
The resolvent function of an operator in a Banach space is defined on an open subset of the complex plane and is holomorphic. It obeys the resolvent equation. A generalization of this equation to Schwartz distributions is defined and a…
Let $A$ be a bounded linear operator on a complex Banach space $X.$ For a given $\alpha \geq 0,$ we consider the class $\mathcal{D}_{A}^{\alpha }\left( \mathbb{R} \right) $ of all bounded linear operators $T$ on $X$ for which there exists a…
The notions of expansivity and positive expansivity for composition operators on Orlicz spaces are investigated. In particular, necessary and sufficient conditions are given for a composition operator to be expansive, positively expansive,…
For any multi-graph $G$ with edge weights and vertex potential, and its universal covering tree $\mathcal{T}$, we completely characterize the point spectrum of operators $A_{\mathcal{T}}$ on $\mathcal{T}$ arising as pull-backs of local,…
It is shown that a positive (bounded linear) operator on a Hilbert space with trivial kernel is unitarily equivalent to a Hankel operator that satisfies double positivity condition if and only if it is non-invertible and has simple spectrum…
We provide conditions for a linear map of the form $C_{R,T}(S)=RST$ to be $q$-frequently hypercyclic on algebras of operators on separable Banach spaces. In particular, if $R$ is a bounded operator satisfying the $q$-Frequent Hypercyclicity…
We consider a first order operator with a periodic 3x3 matrix potential on the real line. This operator appears in the problem of the periodic vector NLS equation. The spectrum of the operator covers the real line, it is union of the…
In this paper, we deal with the construction of holomorphic functions on a simply connected domain satisfying that all its derivatives and antiderivatives under a composition operator have a dense orbit. Such functions will be called Luh…
Resolvents of quasi-linear operators and operator algebras in Banach spaces over the quaternion field are investigated. Spectral theory of unbounded nonlinear operators in quaternion Banach spaces is studied. Strongly continuous semigroups…
In this paper, a criterion for a sequence of composition operators defined on the space of holomorphic functions in a complex domain to be frequently hypercyclic is provided. Such criterion improves some already known special cases and, in…
In this paper we explore the properties of a bounded linear operator defined on a Banach space, in light of operator norm attainment. Using Birkhoff-James orthogonality techniques, we give a necessary condition for a bounded linear operator…
In this paper we completely characterize the norm attainment set of a bounded linear operator on a Hilbert space. This partially answers a question raised recently in [\textit{D. Sain, On the norm attainment set of a bounded linear…
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…
We consider Dirac-like operators with piecewise constant mass terms on spin manifolds, and we study the behaviour of their spectra when the mass parameters become large. In several asymptotic regimes, effective operators appear: the…
We study multi-frequency quasiperiodic Schr\"{o}dinger operators on $\mathbb{Z} $. We prove that for a large real analytic potential satisfying certain restrictions the spectrum consists of a single interval. The result is a consequence of…