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Operators with hypercyclic Cesaro means

2002
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Studia Mathematica
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An operator T on a Banach space B is said to be hypercyclic if there exists a vector x such that the orbit {T n x} n≥1 is dense in B. Hypercyclicity is a strong kind of cyclicity which requires that the linear span of the orbit is dense in B. If the arithmetic means of the orbit of x are dense in B then the operator T is said to be Cesàro-hypercyclic. Apparently Cesàro-hypercyclicity is a strong version of hypercyclicity. We prove that an operator is Cesàro-hypercyclic if and only if there

doi:10.4064/sm152-3-1
fatcat:sulmlgli6zgbzfph276hwiapee