科研之友
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摘要
In this note, we study topologically transitive and hypercyclic composition operators on C-p(X) or C-k(X). We prove that if G is a semigroup of continuous self maps of a countable metric space X with the following properties: (1) every element of G is one-to-one on X, (2) the action of G is strongly run-away on X, then the action of (G) over cap on C-p(X) is topologically transitive and hypercyclic. If G is the set of all one-to-one and continuous self maps of R \ Z, then the action of (G) over cap on C-k(R \ Z) is hypercyclic. We also show that the action of (G) over cap on C-p(omega(1)) is not hypercyclic.
- 出版日期2017
- 单位北京工业大学
