On hypercyclicity and supercyclicity criteria

DOI10.1017/S0004972700035802zbMath1071.47007MaRDI QIDQ4660446

Antonio Bonilla, Teresa Bermúdez, Alfred Peris Manguillot

Publication date: 21 March 2005

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

hypercyclicity criterionsupercyclicity criterionuniversality criterionoperators with dense range

Mathematics Subject Classification ID

Not locally convex spaces (metrizable topological linear spaces, locally bounded spaces, quasi-Banach spaces, etc.) (46A16) Locally convex Fréchet spaces and (DF)-spaces (46A04) Cyclic vectors, hypercyclic and chaotic operators (47A16) Local spectral properties of linear operators (47A11)

Related Items (33)

Linear transitivity criteria ⋮ Chaotic behaviour of birth-and-death models with proliferation ⋮ \(\Gamma\)-supercyclicity ⋮ Disjointness in supercyclicity on the algebra of Hilbert-Schmidt operators ⋮ Common supercyclic vectors for a path of operators ⋮ Distributionally chaotic families of operators on Fréchet spaces ⋮ Unnamed Item ⋮ Supercyclic dynamics of translations on weighted Orlicz spaces ⋮ Subspace-supercyclicity of conditional weighted type translations on \(L^p(G)\) ⋮ Supercyclicity criteria for \(C_0\)-semigroups ⋮ A study of Bishop operators from the point of view of linear dynamics ⋮ Supercyclicity of multiplication on Banach ideal of operators ⋮ Weighted composition operators and supercyclicity criterion ⋮ Disjoint mixing composition operators on the Hardy space in the unit ball ⋮ An extension of hypercyclicity for \(N\)-linear operators ⋮ Disjointness of composition operators onH_v⁰spaces ⋮ On the supercyclicity and hypercyclicity of the operator algebra ⋮ Dynamics of the heat semigroup on symmetric spaces ⋮ Cyclicity of coefficient multipliers: linear structure ⋮ Unnamed Item ⋮ \(n\)-weakly hypercyclic and \(n\)-weakly supercyclic operators ⋮ Dynamics of the Volterra-type integral and differentiation operators on generalized Fock spaces ⋮ Weakly mixing operators on topological vector spaces ⋮ On the universality of multipliers on \(\mathcal H(\mathbb C)\) ⋮ CHAOTIC POLYNOMIALS ON SEQUENCE AND FUNCTION SPACES ⋮ CHAOTIC ASYMPTOTIC BEHAVIOR OF THE HYPERBOLIC HEAT TRANSFER EQUATION SOLUTIONS ⋮ Universal Taylor series with maximal cluster sets ⋮ Distributional chaos for backward shifts ⋮ Dynamics of the differentiation operator on weighted spaces of entire functions ⋮ Unnamed Item ⋮ Existence of hypercyclic polynomials on complex Fréchet spaces ⋮ Existence and nonexistence of hypercyclic semigroups ⋮ Frequently hypercyclic operators

Cites Work

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• Operators with dense, invariant, cyclic vector manifolds
• Hereditarily hypercylic operators
• On operators \(T\) such that \(f(T)\) is hypercyclic
• Sequences of derivatives and normal families
• Sequences of differential operators: exponentials, hypercyclicity and equicontinuity
• Universal Vectors for Operators on Spaces of Holomorphic Functions
• Universal families and hypercyclic operators
• Densely hereditarily hypercyclic sequences and large hypercyclic manifolds
• The Hypercyclicity Criterion for sequences of operators
• Hypercyclic Weighted Shifts
• Supercyclic subspaces: Spectral theory and weighted shifts

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