Dual Hypercyclic Extension for an Operator on a Hilbert Subspace
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.
Chan, Kit C. and Kadel, Gokul R., "Dual Hypercyclic Extension for an Operator on a Hilbert Subspace" (2015). Mathematics and Statistics Faculty Publications. 31.
Houston Journal of Mathematics