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Supercyclic vectors and the Angle Criterion

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Gallardo-Gutiérrez E., Partington J.

Studia Mathematica

2005

tom 166

nr 1

93-99

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.

Ograniczanie wyników

1 Studia Mathematica

1 Gallardo-Gutiérrez E.

1 Partington J.

1 2005

Wyniki wyszukiwania

Supercyclic vectors and the Angle Criterion