Typical operators admit common cyclic vectors

Zorin-Kranich, Pavel

doi:10.1090/S0002-9939-2013-11512-1

Typical operators admit common cyclic vectors
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by Pavel Zorin-Kranich PDF

Proc. Amer. Math. Soc. 141 (2013), 2371-2378 Request permission

Abstract:

Given a countable dense subset $D$ of an infinite-dimensional separable Hilbert space $H$, the set of operators for which every vector in $D$ except zero is hypercyclic (weakly supercyclic) is residual for the strong (resp. weak) operator topology in the unit ball of $L(H)$ multiplied by $R>1$ (resp. $R>0$).

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