On linear operators having supercyclic vectors

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Mathematisches Institut I, Universität Karlsruhe, Postfach 6980, D-7500 Karlsruhe 1, Germany

We show that for a real separable Banach space X there are operators in B(X) having supercyclic vectors if and only if dim X ≤ 2 or dim X = ∞.

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