We provide in this paper a direct and constructive proof of the following fact: for a Banach space X X there are bounded linear operators having hypercyclic vectors if and only if X X is separable and dim X = ∞ \, X = ∞ . This is a special case of a recent result, which in turn solves a problem proposed by S. Rolewicz.
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L. Bernal-González (1999) studied this question.
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