Abstract
Let B(X) be the operator algebra for a separable infinite dimensional Hilbert space H, endowed with the strong operator topology or *-strong topology. We give sufficient conditions for a continuous linear mapping L: B(X) → B(X) to be supercyclic or *-supercyclic. In particular our condition implies the existence of an infinite dimensional subspace of supercyclic vectors for a mapping T on H. Hypercyclicity of the operator algebra with strong operator topology was studied by Chan and here we obtain an analogous result in the case of *-strong operator topology.
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Dedicated to Mola Ali
This paper is a part of the second author’s doctoral thesis, written at Shiraz University under the direction of the first author
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Yousefi, B., Rezaei, H. On the supercyclicity and hypercyclicity of the operator algebra. Acta. Math. Sin.-English Ser. 24, 1221–1232 (2008). https://doi.org/10.1007/s10114-007-6601-2
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DOI: https://doi.org/10.1007/s10114-007-6601-2
Keywords
- operator algebra
- *-strong topology
- strong operator topology
- hypercyclicity criterion
- supercyclicity criterion