Typical operators admit common cyclic vectors
arXiv:1008.2878 · doi:10.1090/S0002-9939-2013-11512-1
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)
7 pages, incorporating the referee's suggestions