C 0 -continuity of the Fröbenius-Perron semigroup

Andrés Navas and Sergio Plaza

International Journal of Mathematics and Mathematical Sciences, 2002, vol. 31, 1-13

Abstract:

We consider the Fröbenius-Perron semigroup of linear operators associated to a semidynamical system defined in a topological space X endowed with a finite or a σ -finite regular measure. We prove that if there exists a faithful invariant measure for the semidynamical system, then the Fröbenius-Perron semigroup of linear operators is C 0 -continuous in the space L μ   1 ( X ) . We also give a geometrical condition which ensures C 0 -continuity of the Fröbenius-Perron semigroup of linear operators in the space L μ   p ( X ) for 1 ≤ p < ∞ , as well as in the space L loc   1 .

Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:689242

DOI: 10.1155/S0161171202013364

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