On hypercyclic operators on Banach spaces

Bernal-González, Luis

doi:10.1090/S0002-9939-99-04657-2

On hypercyclic operators on Banach spaces
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Proc. Amer. Math. Soc. 127 (1999), 1003-1010 Request permission

Abstract:

We provide in this paper a direct and constructive proof of the following fact: for a Banach space $X$ there are bounded linear operators having hypercyclic vectors if and only if $X$ is separable and dim$X = \infty$. This is a special case of a recent result, which in turn solves a problem proposed by S. Rolewicz.

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