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Supercyclicity in the operator algebra

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Montes-Rodríguez A., Romero-Moreno M.

Studia Mathematica

2002

tom 150

nr 3

201-213

We prove a Supercyclicity Criterion for a continuous linear mapping that is defined on the operator algebra of a separable Banach space ℬ. Our result extends a recent result on hypercyclicity on the operator algebra of a Hilbert space. This kind of result is a powerful tool to analyze the structure of supercyclic vectors of a supercyclic operator that is defined on ℬ. For instance, as a consequence of the main result, we give a very simple proof of the recently established fact that certain supercyclic operators defined on a Banach space have an infinite-dimensional closed subspace of supercyclic vectors.

Ograniczanie wyników

1 Studia Mathematica

1 Montes-Rodríguez A.

1 Romero-Moreno M.

1 2002

Wyniki wyszukiwania

Supercyclicity in the operator algebra