Supercyclic vectors and the Angle Criterion

• Autorzy: Eva A. Gallardo-Gutiérrez , Jonathan R. Partington
• Języki publikacji: EN

Abstrakty

EN

We show that the Angle Criterion for testing supercyclic vectors depends in an essential way on the geometrical properties of the underlying space. In particular, we exhibit non-supercyclic vectors for the backward shift acting on c₀ that still satisfy such a criterion. Nevertheless, if ℬ is a locally uniformly convex Banach space, the Angle Criterion yields an equivalent condition for a vector to be supercyclic. Furthermore, we prove that local uniform convexity cannot be weakened to strict convexity.

Kategorie tematyczne

• 47A16: Cyclic vectors, hypercyclic and chaotic operators
• 47A15: Invariant subspaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2005
• Tom: 166
• Numer: 1
• Strony: 93-99

Daty

wydano

2005

Twórcy

autor

Eva A. Gallardo-Gutiérrez

• Departamento de Matemáticas, Universidad de Zaragoza, Plaza San Francisco s/n, 50009 Zaragoza, Spain

autor

Jonathan R. Partington

• School of Mathematics, University of Leeds, Leeds LS2 9JT, U.K.

Identyfikatory

DOI

10.4064/sm166-1-7