Invariant manifolds of hypercyclic vectors

Bourdon, Paul S.

doi:10.1090/S0002-9939-1993-1148021-4

Invariant manifolds of hypercyclic vectors
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Proc. Amer. Math. Soc. 118 (1993), 845-847 Request permission

Abstract:

We show that any hypercyclic operator on Hilbert space has a dense, invariant linear manifold consisting, except for zero, entirely of hypercyclic vectors.

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