SPECTRUM OF HYPERCYCLIC AND SUPERCYCLIC OPERATORS

Juan J. Sánchez

   A bounded linear operator T on a Banach space B is called hypercyclic if there exists x ∈ B such that the orbit {Tⁿ x : n ≥ 0} is dense in B. If the scalar multiples of the elements in the orbit are dense, then the operator T is called supercyclic. We give some general spectral properties for these "wild" operators. We disccuss the spectrum of hypercyclic and supercyclic operators and we will see that these classes of operators have dierent spectral behavior. Finally, we analyze the growth of the resolvent of the hypercyclic and supercyclic operators.

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