Dense range perturbations of hypercyclic operators

• Autorzy: Luis Bernal-Gonzalez
• Języki publikacji: EN

Abstrakty

EN

We show that if (Tₙ) is a hypercyclic sequence of linear operators on a locally convex space and (Sₙ) is a sequence of linear operators such that the image of each orbit under every linear functional is non-dense then the sequence (Tₙ + Sₙ) has dense range. Furthermore, it is proved that if T,S are commuting linear operators in such a way that T is hypercyclic and all orbits under S satisfy the above non-denseness property then T - S has dense range. Corresponding statements for operators and sequences which are hypercyclic in a weaker sense are shown. Our results extend and improve a result on denseness due to C. Kitai.

Kategorie tematyczne

• 47A05: General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
• 47A16: Cyclic vectors, hypercyclic and chaotic operators
• 47A55: Perturbation theory
• 46A03: General theory of locally convex spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2002
• Tom: 91
• Numer: 2
• Strony: 283-292

Daty

wydano

2002

Twórcy

autor

Luis Bernal-Gonzalez

• Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, Apdo. 1160, Avenida Reina Mercedes, 41080 Sevilla, Spain

Identyfikatory

DOI

10.4064/cm91-2-7