50 citations · 193 across the 24 of their papers we have counts for
26 papers
The spectrum of operator extensions to free Banach Lattices
Jochen Glück, Phillip Krokor
Every bounded linear operator on a complex Banach space is known to extend to a lattice homomorphism that acts on the so-called complex free Banach lattice o…
A note on the positivity of inverse operators acting on -algebras
Jochen Glück, Ulrich Groh
For a positive and invertible linear operator acting on a -algebra, we give necessary and sufficient criteria for the inverse operator to be positive, too. Moreov…
Non-Positivity of the heat equation with non-local Robin boundary conditions
Jochen Glück, Jonathan Mui
We study heat equations on bounded Lipschitz domains , where is a second-order uniform…
Limit-case admissibility for positive infinite-dimensional systems
Sahiba Arora, Jochen Glück, Lassi Paunonen +1
In the context of positive infinite-dimensional linear systems, we systematically study -admissible control and observation operators with respect to the limit-cases $p=\infty…
Eventual cone invariance revisited
Jochen Glück, Julian Hölz
We consider finite-dimensional real vector spaces ordered by a closed cone with non-empty interior and study eventual nonnegativity of matrix semigroups $(e^{tA})_{t \ge…
Stability via closure relations with applications to dissipative and port-Hamiltonian systems
Jochen Glück, Birgit Jacob, Annika Meyer +2
We consider differential operators that can be represented by means of a so-called closure relation in terms of a simpler operator defined on a larger…
Order boundedness and order continuity properties of positive operator semigroups
Jochen Glück, Michael Kaplin
Relatively uniformly continuous (ruc) semigroups were recently introduced and studied by Kandić, Kramar-Fijavž, and the second-named author, in order to make the theory of one-para…
Stability criteria for positive semigroups on ordered Banach spaces
Jochen Glück, Andrii Mironchenko
We consider generators of positive -semigroups and, more generally, resolvent positive operators on ordered Banach spaces and seek for conditions ensuring the negativity o…
Aperiodicity of positive operators that increase the support of functions
Jochen Glück
Consider a positive operator on an -space (or, more generally, a Banach lattice) which increases the support of functions in the sense that fo…
Convergence to equilibrium for linear parabolic systems coupled by matrix-valued potentials
Alexander Dobrick, Jochen Glück
We consider systems of parabolic linear equations, subject to Neumann boundary conditions on bounded domains in , that are coupled by a matrix-valued potential , a…
A characterization of the individual maximum and anti-maximum principle
Sahiba Arora, Jochen Glück
Abstract approaches to maximum and anti-maximum principles for differential operators typically rely on the condition that all vectors in the domain of the operator are dominated b…
Local uniform convergence and eventual positivity of solutions to biharmonic heat equations
Daniel Daners, Jochen Glück, Jonathan Mui
We study the evolution equation associated with the biharmonic operator on infinite cylinders with bounded smooth cross-section subject to Dirichlet boundary conditions. The focus…
Stability of (eventually) positive semigroups on spaces of continuous functions
Sahiba Arora, Jochen Glück
We present a new and very short proof of the fact that, for positive -semigroups on spaces of continuous functions, the spectral and the growth bound coincide. Our argument, i…
An operator theoretic approach to uniform (anti-)maximum principles
Sahiba Arora, Jochen Glück
Maximum principles and uniform anti-maximum principles are a ubiquitous topic in PDE theory that is closely tied to the Krein--Rutman theorem and kernel estimates for resolvents. W…
Spectrum and convergence of eventually positive operator semigroups
Sahiba Arora, Jochen Glück
An intriguing feature of positive -semigroups on function spaces (or more generally on Banach lattices) is that their long-time behaviour is much easier to describe than it is…
Nonlinear small-gain theorems for input-to-state stability of infinite interconnections
Andrii Mironchenko, Christoph Kawan, Jochen Glück
We consider infinite heterogeneous networks, consisting of input-to-state stable subsystems of possibly infinite dimension. We show that the network is input-to-state stable, provi…
Positive irreducible semigroups and their long-time behaviour
Wolfgang Arendt, Jochen Glück
The notion \emph{Perron-Frobenius theory} usually refers to the interaction between three properties of operator semigroups: positivity, spectrum and long-time behaviour. These int…
Stability of transition semigroups and applications to parabolic equations
Moritz Gerlach, Jochen Glück, Markus Kunze
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 wi…
A criterion for the uniform eventual positivity of operator semigroups
Daniel Daners, Jochen Glück
Consider a -semigroup on a function space or, more generally, on a Banach lattice . We prove a sufficient criterion for the operators to be po…
A Toolkit for Constructing Dilations on Banach Spaces
Stephan Fackler, Jochen Glück
We present a completely new structure theoretic approach to the dilation theory of linear operators. Our main result is the following theorem: if is a super-reflexive Banach sp…
Mean ergodicity vs weak almost periodicity
Moritz Gerlach, Jochen Glück
We provide explicit examples of positive and power-bounded operators on and which are mean ergodic but not weakly almost periodic. As a consequence we prove tha…
Convergence of Positive Operator Semigroups
Moritz Gerlach, Jochen Glück
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 spl…
The role of domination and smoothing conditions in the theory of eventually positive semigroups
Daniel Daners, Jochen Glück
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…
Eventually Positive Semigroups of Linear Operators
Daniel Daners, Jochen Glück, James B. Kennedy
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 positiv…