A Hypercyclic Operator whose Adjoint is Also Hypercyclic

DOI10.2307/2048699zbMath0748.47023OpenAlexW4233293104MaRDI QIDQ3981090

Héctor N. Salas

Publication date: 26 June 1992

Full work available at URL: https://doi.org/10.2307/2048699

zbMATH Keywords

bilateral shifthypercylic operator

Mathematics Subject Classification ID

Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.) (47B37) Special classes of linear operators (47B99)

Related Items (34)

Hypercyclic Weighted Shifts ⋮ Universal families and hypercyclic operators ⋮ Disjointness in hypercyclicity ⋮ Chaotic unilateral weighted backward shifts on sequentially complete topological sequence spaces ⋮ Linear structure of hypercyclic vectors ⋮ Dual disjoint hypercyclic operators ⋮ Set-valued chaos in linear dynamics ⋮ Unnamed Item ⋮ Dynamics of weighted shifts on directed trees ⋮ Topological properties of weighted composition operators in sequence spaces ⋮ Residuality of sets of hypercyclic operators ⋮ Numerically hypercyclic operators ⋮ Chaotic weighted translations on groups ⋮ Limits of hypercyclic and supercyclic operators ⋮ Hypercyclic operators failing the hypercyclicity criterion on classical Banach spaces ⋮ Explicit constructions of dense common hypercyclic subspaces ⋮ On the chaoticity of some tensor product weighted backward shift operators acting on some tensor product Fock-Bargmann spaces ⋮ Unnamed Item ⋮ Hypercyclicity properties of commutator maps ⋮ Some necessary and sufficient conditions for hypercyclicity criterion ⋮ Two remarks on frequent hypercyclicity ⋮ On linear dynamics of sets of operators ⋮ Supercyclic subspaces: Spectral theory and weighted shifts ⋮ BANACH SPACES WITH SEPARABLE DUALS SUPPORT DUAL HYPERCYCLIC OPERATORS ⋮ Simultaneous chaotic extensions for general operators on a Hilbert subspace ⋮ Some basic properties of hypercyclic operators ⋮ k-diskcyclic operators on Banach spaces ⋮ Linear dynamical systems on Hilbert spaces: typical properties and explicit examples ⋮ Prescribed compressions of dual hypercyclic operators ⋮ On operators \(T\) such that \(f(T)\) is hypercyclic ⋮ Orbital and spectral aspects of hypercyclic operators and semigroups ⋮ Hereditarily hypercylic operators ⋮ Operators with dense, invariant, cyclic vector manifolds ⋮ Spectral theory and hypercyclic subspaces

Cites Work

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• Operators with dense, invariant, cyclic vector manifolds
• On the multiplicity of T\(\oplus T\oplus \cdot \cdot \cdot \oplus T\)
• On Orbits of Linear Operators
• Universal Vectors for Operators on Spaces of Holomorphic Functions
• The Diagonal Entries in the Formula `Quasitriangular - Compact = Triangular', and Restrictions of Quasitriangularity

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