C0-continuity of the Fröbenius-perron Semigroup
نویسندگان
چکیده
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 C0-continuous in the space Lμ(X). We also give a geometrical condition which ensures C0-continuity of the Fröbenius-Perron semigroup of linear operators in the space Lμ(X) for 1≤ p <∞, as well as in the space Lloc.
منابع مشابه
Ergodic Properties of the Fröbenius–Perron Semigroup
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. Assuming strong continuity for the Fröbenius–Perron semigroup of linear operators in the space Lμ(X) or in the space Lμ(X) for 1 < p <∞ ([11]). We study in this article ergodic properties of the Fröbenius–Perron...
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