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Spectral theory and hypercyclic subspaces

2000
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Transactions of the American Mathematical Society
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A vector x in a Hilbert space H is called hypercyclic for a bounded operator T : H → H if the orbit {T n x : n ≥ 1} is dense in H. Our main result states that if T satisfies the Hypercyclicity Criterion and the essential spectrum intersects the closed unit disk, then there is an infinite-dimensional closed subspace consisting, except for zero, entirely of hypercyclic vectors for T . The converse is true even if T is a hypercyclic operator which does not satisfy the Hypercyclicity Criterion. As

doi:10.1090/s0002-9947-00-02743-4
fatcat:kainhzh3nnhznbf2npp2gys2lm