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Full-Text Articles in Mathematics
Difference Of Two Weighted Composition Operators On Bergman Spaces, S. Acharyya, Z. Wu
Difference Of Two Weighted Composition Operators On Bergman Spaces, S. Acharyya, Z. Wu
Publications
Following the techniques developed by Moorhouse and Saukko, the authors characterize the compactness of the difference of two weighted composition operators acting between different weighted Bergman spaces, under certain restrictions on the weights.
Difference Of Two Weighted Composition Operators On Bergman Spaces, Soumyadip Acharyya, Zhijian Wu
Difference Of Two Weighted Composition Operators On Bergman Spaces, Soumyadip Acharyya, Zhijian Wu
Soumyadip Acharyya
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.
Nonminimal Cyclic Invariant Subspaces Of Hyperbolic Composition Operators, Valentin Matache
Nonminimal Cyclic Invariant Subspaces Of Hyperbolic Composition Operators, Valentin Matache
Mathematics Faculty Publications
Operators on function spaces acting by composition to the right with a fixed self-map ϕ are called composition operators. We denote them Cϕ. Given ϕ, a hyperbolic disc automorphism, the composition operator Cϕ on the Hilbert Hardy space H2 is considered. The bilateral cyclic invariant subspaces Kf, f ∈ H2, of Cϕ are studied, given their connection with the invariant subspace problem, which is still open for Hilbert space operators. We prove that nonconstant inner functions u induce non–minimal cyclic subspaces Ku if they have unimodular, orbital, cluster points. Other results about Ku when u is inner are obtained. If …
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 …