In:
Journal of Operator Theory, Theta Foundation, Vol. 88, No. 1 ( 2022-07-15), p. 205-244
Abstract:
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. A drawback of the present theory of eventually positive C0-semigroups is that it is applicable only when the leading eigenvalue of the semigroup generator has a strongly positive eigenvector. We weaken this requirement and give sufficient criteria for individual and uniform local eventual positivity of the semigroup. This allows us to treat a larger class of examples by giving us more freedom on the domain when dealing with function spaces − for instance, the square of the Laplace operator with Dirichlet boundary conditions on L2 and the Dirichlet bi-Laplacian on Lp-spaces. Besides, we establish various spectral and convergence properties of locally eventually positive semigroups.
Type of Medium:
Online Resource
ISSN:
0379-4024
,
1841-7744
DOI:
10.7900/jot.y2022v088i01
DOI:
10.7900/jot.2021jan26.2316
Language:
Unknown
Publisher:
Theta Foundation
Publication Date:
2022
detail.hit.zdb_id:
2043904-0
SSG:
17,1
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