We transfer a number of fundamental results about hypercyclic operators on locally convex spaces (due to Ansari, Bès, Bourdon, Costakis, Feldman, and Peris) to the non-locally convex situation. This answers a problem posed by A. Peris [ Multi-hypercyclic operators are hypercyclic , Math. Z. 236 (2001), 779-786].
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Jochen Wengenroth (2003) studied this question.