We initiate a theory of locally eventually positive operator semigroups on Banach lattices. Intuitively this means: given a positive initial datum, the solution of the corresponding Cauchy problem becomes (and stays) positive in a part of the domain, after a sufficiently large time. We give sufficient criteria for local eventual positivity of the semigroup and apply them to concrete operators, for instance, the square of the Dirichlet Laplacian on L 2 and the Dirichlet bi-Laplacian on L p-spaces. Besides, we establish various spectral and convergence properties of locally eventually positive semigroups.
|Number of pages||40|
|Journal||Journal of Operator Theory|
|Publication status||Published - 2022|
DFG Classification of Subject Areas according to Review Boards
- C_0-semigroup, local eventual positivity, One parameter semigroups of linear operators, Antimaximum principle, Eventually positive resolvent, Eventually positive semigroup, Locally eventually positive resolvent, Locally eventually positive semigroup, Positive spectral projection, semigroups on Banach lattices