Related papers: Towards a Perron--Frobenius Theory for Eventually …
A generalized Krein-Rutman theorem for a strongly positive bounded linear operator whose spectral radius is larger than essential spectral radius is established: the spectral radius of the operator is an algebraically simple eigenvalue with…
To study the convergence to equilibrium in random maps we developed the spectral theory of the corresponding transfer (Perron-Frobenius) operators acting in a certain Banach space of generalized functions. The random maps under study in a…
This paper investigates spectral properties of certain classes of positive operators originated from different matrices appeared in linear complementarity problem. These positive operators play a crucial role in various areas of mathematics…
Positive $C_0$-semigroups that occur in concrete applications are, more often than not, irreducible. Therefore a deep and extensive theory of irreducibility has been developed that includes characterizations, perturbation analysis, and…
We study ordinal-indexed, multi-layer iterations of bounded operator transforms and prove convergence to spectral/ergodic projections under functional-calculus hypotheses. For normal operators on Hilbert space and polynomial or holomorphic…
Given a Hilbert space operator $T$, the level sets of function $\Psi_T(z)=\|(T-z)^{-1}\|^{-1}$ determine the so-called pseudospectra of $T$. We set $\Psi_T$ to be zero on the spectrum of $T$. After giving some elementary properties of…
We exhibit a general class of unbounded operators in Banach spaces which can be shown to have the single-valued extension property, and for which the local spectrum at suitable points can be determined. We show that a local spectral radius…
Nonlinearities in finite dimensions can be linearized by projecting them into infinite dimensions. Unfortunately, often the linear operator techniques that one would then use simply fail since the operators cannot be diagonalized. This…
In this paper, we investigate the well-posedness and positivity property of infinite-dimensional linear system with unbounded input and output operators. In particular, we characterize the internal and external positivity for this class of…
Let $T\colon X\to X$ be a bounded operator on Banach space, whose spectrum $\sigma(T)$ is included in the closed unit disc $\overline{\mathbb D}$. Assume that the peripheral spectrum $\sigma(T)\cap{\mathbb T}$ is finite and that $T$…
We obtain a solution to the Bessis-Moussa-Villani conjecture for a trace-class perturbation of a semi-bounded operator and answer affirmatively the question on positivity of higher order spectral shift functions in the setting of…
In this paper we derive novel families of inclusion sets for the spectrum and pseudospectrum of large classes of bounded linear operators, and establish convergence of particular sequences of these inclusion sets to the spectrum or…
In \cite{Os} a general spectral approximation theory was developed for compact operators on a Banach space which does not require that the operators be self-adjoint and also provides a first order correction term. Here we extend some of the…
We propose a new approach to the spectral theory of perturbed linear operators , in the case of a simple isolated eigenvalue. We obtain two kind of results: ''radius bounds'' which ensure perturbation theory applies for perturbations up to…
Positive definite functions are fundamental to many areas of applied mathematics, probability theory, spatial statistics and machine learning, amogst others. Motivated by a problem coming from the maximum likelihood estimation under fixed…
We define essentially positive operators on Hilbert space as a class of self-adjoint operators whose essential spectra is contained in the nonnegative real numbers and describe their basic properties. Using Toeplitz operators and the…
We establish a spectral characterization theorem for the operators on complex Hilbert spaces of arbitrary dimensions that attain their norm on every closed subspace. The class of these operators is not closed under addition. Nevertheless,…
We introduce complex cones and associated projective gauges, generalizing a real Birkhoff cone and its Hilbert metric to complex vector spaces. We deduce a variety of spectral gap theorems in complex Banach spaces. We prove a dominated…
We introduce the super-shadowing property in linear dynamics, where pseudotrajectories are approximated by sequences of the form $(\lambda_nT^nx)$, with $(\lambda_n)_n$ being complex scalars. For compact operators on Banach spaces, we…
We consider finite-dimensional real vector spaces $X$ ordered by a closed cone $X_+$ with non-empty interior and study eventual nonnegativity of matrix semigroups $(e^{tA})_{t \ge 0}$ with respect to this cone. Our first contribution is the…