Hypercyclic property of weighted composition operators

DOI10.1090/S0002-9939-07-08833-8zbMath1129.47010OpenAlexW2005930343MaRDI QIDQ5295109

Bahmann Yousefi, Hamid Rezaei

Publication date: 27 July 2007

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-07-08833-8

zbMATH Keywords

weighted composition operatorshypercyclic operatorDenjoy-Wolff pointlinear-fractional model theoremSchwarz's LemmaJulia-Carathéodory theorem

Mathematics Subject Classification ID

Linear operators on function spaces (general) (47B38) Linear composition operators (47B33) Cyclic vectors, hypercyclic and chaotic operators (47A16)

Related Items (34)

Dynamical properties of weighted composition operators on the space of smooth functions ⋮ Hypercyclicity of weighted composition operators on \(L^p\)-spaces ⋮ Notes on hypercyclicity of composition operator on the weighted Dirichlet spaces ⋮ Dynamics of composition operators on Hilbert spaces of Dirichlet series ⋮ Reproducing kernel Hilbert spaces supporting nontrivial Hermitian weighted composition operators ⋮ Dynamics of composition operators with holomorphic symbol ⋮ Unnamed Item ⋮ Non-weakly supercyclic weighted composition operators ⋮ Disjoint mixing linear fractional composition operators in the unit ball ⋮ Dynamics of weighted composition operators in the unit ball ⋮ Dynamics of weighted composition operators ⋮ Chaotic Dynamics of Composition Operators on the Space of Continuous Functions ⋮ Disjoint hypercyclicity of weighted composition operators ⋮ Weighted composition operators and supercyclicity criterion ⋮ Weighted composition operators between different Fock spaces ⋮ Frequent hypercyclicity of weighted composition operators on the space of smooth functions ⋮ Hypercyclic linear fractional composition operators on weighted Dirichlet spaces \(\mathcal{D}_\alpha^p\) ⋮ Hereditarily transitive tuples ⋮ On the supercyclicity and hypercyclicity of the operator algebra ⋮ Disjoint Hypercyclicity and Topological Entropy of Composition Operators ⋮ Complex symmetric weighted composition operators on \(H^2(\mathbb{D})\) ⋮ Hypercyclicity of weighted composition operators on a weighted Dirichlet space ⋮ Weighted composition operators on Fock spaces and their dynamics ⋮ Supercyclicity in the operator algebra using Hilbert-Schmidt operators ⋮ Hypercyclicity of weighted composition operators on the weighted little Bloch space ⋮ Unnamed Item ⋮ Complex symmetric weighted composition operators on Dirichlet spaces and Hardy spaces in the unit ball ⋮ Dynamics of weighted composition operators on function spaces defined by local properties ⋮ Universal functions for composition operators with non-automorphic symbol ⋮ Hypercyclicity of the adjoint of weighted composition operators ⋮ Cyclicity of the adjoint of weighted composition operators on the hilbert space of analytic functions ⋮ Supercyclicity of weighted composition operators on spaces of continuous functions ⋮ Hypercyclic composition operators with automorphisms of the upper half-plane ⋮ Characterization of hypercyclic weighted composition operators on the space of holomorphic functions

Cites Work

• Operators with dense, invariant, cyclic vector manifolds
• Composition operators and classical function theory
• The numerical ranges of automorphic composition operators
• Rotations of hypercyclic and supercyclic operators
• Some necessary and sufficient conditions for hypercyclicity criterion
• Cyclic phenomena for composition operators
• Universal Vectors for Operators on Spaces of Holomorphic Functions
• Universal families and hypercyclic operators
• Hypercyclic Weighted Shifts
• On orbits of elements
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