Related papers: Positive irreducible semigroups and their long-tim…

We consider eventually positive operator semigroups and study the question whether their eventual positivity is preserved by bounded perturbations of the generator or not. We demonstrate that eventual positivity is not stable with respect…

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…

The paper deals with the long-term behavior of positive operator semigroups on spaces of bounded functions and of signed measures, which have applications to parabolic equations with unbounded coefficients and to stochastic analysis. The…

We develop a systematic theory of eventually positive semigroups of linear operators mainly on spaces of continuous functions. By eventually positive we mean that for every positive initial condition the solution to the corresponding Cauchy…

The spectral theory of semigroup generators is a crucial tool for analysing the asymptotic properties of operator semigroups. Typically, Tauberian theorems, such as the ABLV theorem, demand extensive information about the spectrum to derive…

We present new conditions for semigroups of positive operators to converge strongly as time tends to infinity. Our proofs are based on a novel approach combining the well-known splitting theorem by Jacobs, de Leeuw and Glicksberg with a…

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…

An intriguing feature of positive $C_0$-semigroups on function spaces (or more generally on Banach lattices) is that their long-time behaviour is much easier to describe than it is for general semigroups. In particular, the convergence of…

This article is a contribution to the spectral theory of so-called eventually positive operators, i.e.\ operators $T$ which may not be positive but whose powers $T^n$ become positive for large enough $n$. While the spectral theory of such…

We consider positive operator semigroups on ordered Banach spac\-es and study the relation of their long time behaviour to two different domination properties. First, we analyse under which conditions almost periodicity and mean ergodicity…

We perform an in-depth study of some domination and smoothing properties of linear operators and of their role within the theory of eventually positive operator semigroups. On the one hand we prove that, on many important function spaces,…

The stability and contraction properties of positive integral semigroups on Polish spaces are investigated. Our novel analysis is based on the extension of V-norm contraction methods, associated to functionally weighted Banach spaces for…

Let $P^V_t$, $t\ge0$, be the Schrodinger semigroup associated to a potential $V$ and Markov semigroup $P_t$, $t\ge0$, on $C(X)$. Existence is established of a left eigenvector and right eigenvector corresponding to the spectral radius…

In a couple of previous papers, we initiated a systematic study of semihypergroups and had a thorough discussion on certain analytic and algebraic aspects associated to this class of objects. In this article, we introduce and examine…

We give extensions of results on nonnegative matrix semigroups which deduce finiteness or boundedness of such semigroups from the corresponding local properties, e.g., from finiteness or boundedness of values of certain linear functionals…

Large time behaviour of heat semigroups (and more generally, of positive selfadjoint semigroups) is studied. Convergence of the semigroup to the ground state and of averaged logarithms of kernels to the ground state energy is shown in the…

We investigate a smoothing property for strongly-continuous operator semigroups, akin to ultracontractivity in parabolic evolution equations. Specifically, we establish the stability of this property under certain relatively bounded…

The paper introduces and studies differentially positive systems, that is, systems whose linearization along an arbitrary trajectory is positive. A generalization of Perron Frobenius theory is developed in this differential framework to…

We develop a Perron-Frobenius type theory for products of random quantum channels acting on finite-dimensional matrix algebras sampled from a stationary and ergodic stochastic process, which, in keeping with the literature, we call ergodic…

In this article we revisit a new notion of positivity in real semisimple Lie groups that at the same time generalizes total positivity in split real Lie groups as well as positive Lie semigroups in Hermitian Lie groups of tube type. We…