Dual Hypercyclic Extension for an Operator on a Hilbert Subspace
Kit Chak Chan, Gokul R. Kadel · ScholarWorks@BGSU (Bowling Green State University) · 2015
Let M be a closed nontrivial subspace of a separable, infinite dimensional Hilbert space H with dim(H/M) = ∞. We show that a bounded linear operator A : M → M has a dual hypercyclic extension T : H → H if and only if its adjoint A∗ : M → M is hypercyclic.