Somewhere dense orbits are everywhere dense

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Hypercyclic tuples of operators and somewhere dense orbits (2008, background): “The next lemma is similar to one from Bourdon and Feldman [5].”
Hypercyclic operators on non-locally convex spaces (2003, background): “Feldman [4] even showed that Orb(〈x〉) is either everywhere dense”
Disjointness in hypercyclicity (2007, result): “The following proposition is a slight modification of [25, Theorem 2.5] by Salas and of [9, Theorem 4.2] by Feldman.”
HYPERCYCLIC OPERATORS, MIXING OPERATORS AND THE BOUNDED STEPS PROBLEM (2005, result): “This is also the case for the results [13], [29] and [12], which yield Ansari’s result as a corollary.”
On the spectrum of frequently hypercyclic operators (2008, methodology): “This obstacle was removed by Wengenroth [26], which allowed him to extend the Bourdon and Feldman theorem to arbitrary topological vector spaces, see also the survey [18].”
Frequently dense orbits (2005, background): “By a theorem of Bourdon and Feldman [6], an operator on a separable locally convex space is hypercyclic as soon as it has a somewhere dense orbit; in fact, the assumption of local convexity may be dropped, cf. Wengenroth [11].”