A criterion for the uniform eventual positivity of operator semigroups

Abstract

Consider a $C_0$-semigroup $(e^{tA}{)}_{t\ge 0}$ on a function space or, more generally, on a Banach lattice $E$. We prove a sufficient criterion for the operators $e^{tA}$ to be positive for all sufficiently large times $t$, while the semigroup itself might not be positive. This complements recently established criteria for the individual orbits of the semigroup to become eventually positive for all positive initial values. We apply our main result to study the qualitative behaviour of the solutions to various partial differential equations.

18 pages

References in corpus (3)

• Eventually Positive Semigroups of Linear Operators
• Eventually and asymptotically positive semigroups on Banach lattices
• The role of domination and smoothing conditions in the theory of eventually positive semigroups

Cited by in corpus (11)

• The Bi-Laplacian with Wentzell boundary conditions on Lipschitz domains
• Locally Eventually Positive Operator Semigroups
• Spectrum and convergence of eventually positive operator semigroups
• Stability of uniformly eventually positive $C_0$-semigroups on $L_p$-spaces
• Positive irreducible semigroups and their long-time behaviour
• Spectral properties of locally eventually positive operator semigroups
• An operator theoretic approach to uniform (anti-)maximum principles
• Local uniform convergence and eventual positivity of solutions to biharmonic heat equations
• Criteria for eventual domination of operator semigroups and resolvents
• Domination of semigroups generated by regular forms
• A characterization of the individual maximum and anti-maximum principle