Hereditarily hypercyclic subspaces

الأصل · EN

We say that a sequence of operators (Tₙ) possesses hereditarily hypercyclic subspaces along a sequence (nₖ) if for any subsequence (mₖ)⊂(nₖ), the sequence (Tₘₖ) possesses a hypercyclic subspace. While so far no characterization of the existence of hypercyclic subspaces in the case of Fréchet spaces is known, we succeed to obtain a characterization of sequences (Tₙ) possessing hereditarily hypercyclic subspaces along (nₖ), under the assumption that the sequence (Tₙ) satisfies the Hypercyclicity Criterion along (nₖ). We also obtain a characterization of operators possessing a hypercyclic subspace under the assumption that T satisfies the Frequent Hypercyclicity Criterion.