Chaotic polynomials on Fréchet spaces

Peris, Alfredo

doi:10.1090/S0002-9939-99-04937-0

Chaotic polynomials on Fréchet spaces
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by Alfredo Peris PDF

Proc. Amer. Math. Soc. 127 (1999), 3601-3603 Request permission

Erratum: Proc. Amer. Math. Soc. 129 (2001), 3759-3760.

Abstract:

Contrary to the case of polynomials on Banach spaces, in which it is known that no hypercyclic homogeneous polynomial of degree $m \geq 2$ exists on any Banach space, we construct for each $m \geq 2$ a chaotic $m$-homogeneous polynomial $P$ on the Fréchet space $\mathcal {H}(\mathbb {C} )$.

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