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Dense range perturbations of hypercyclic operators

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Bernal-Gonzalez L.

Colloquium Mathematicum

2002

tom 91

nr 2

283-292

We show that if (Tₙ) is a hypercyclic sequence of linear operators on a locally convex space and (Sₙ) is a sequence of linear operators such that the image of each orbit under every linear functional is non-dense then the sequence (Tₙ + Sₙ) has dense range. Furthermore, it is proved that if T,S are commuting linear operators in such a way that T is hypercyclic and all orbits under S satisfy the above non-denseness property then T - S has dense range. Corresponding statements for operators and sequences which are hypercyclic in a weaker sense are shown. Our results extend and improve a result on denseness due to C. Kitai.

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1 Colloquium Mathematicum

1 Bernal-Gonzalez L.

1 2002

Wyniki wyszukiwania

Dense range perturbations of hypercyclic operators