On the supercyclicity and hypercyclicity of the operator algebra |
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Authors: | B Yousefi H Rezaei |
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Institution: | (1) Department of Mathematics, College of Sciences, Shiraz University, Shiraz, 71454, Iran;(2) Department of Mathematics, Payame-Noor University, Tehran, Iran |
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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.
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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Keywords: | operator algebra *-strong topology strong operator topology hypercyclicity criterion supercyclicity criterion |
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