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Full-Text Articles in Physical Sciences and Mathematics
Sufficient Conditions On Nonunitary Operators That Imply The Unitary Operators, Pabitra Kumar Jena
Sufficient Conditions On Nonunitary Operators That Imply The Unitary Operators, Pabitra Kumar Jena
Turkish Journal of Mathematics
In this paper, we give sufficient conditions on nonunitary operators on the Bergman space that imply the unitary operators.
A Note On Dynamics In Functional Spaces, Liangxue Peng, Chong Yang
A Note On Dynamics In Functional Spaces, Liangxue Peng, Chong Yang
Turkish Journal of Mathematics
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 $\hat{G}$ on $C_p(X)$ is topologically transitive and hypercyclic. If $G$ is the set of all one-to-one and continuous self maps of $\mathbb{R}\setminus \mathbb{Z}$, then the action of $\hat{G}$ on $C_k(\mathbb{R}\setminus \mathbb{Z})$ is hypercyclic. We also show that the action of …