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 = ∞.
@article{bwmeta1.element.bwnjournal-article-smv103i3p295bwm, author = {Gerd Herzog}, title = {On linear operators having supercyclic vectors}, journal = {Studia Mathematica}, volume = {103}, year = {1992}, pages = {295-298}, zbl = {0811.47018}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv103i3p295bwm} }
Herzog, Gerd. On linear operators having supercyclic vectors. Studia Mathematica, Tome 103 (1992) pp. 295-298. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv103i3p295bwm/
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