347 research outputs found
Hypercyclic operators on topological vector spaces
Bonet, Frerick, Peris and Wengenroth constructed a hypercyclic operator on
the locally convex direct sum of countably many copies of the Banach space
. We extend this result. In particular, we show that there is a
hypercyclic operator on the locally convex direct sum of a sequence
of Fr\'echet spaces if and only if each is separable
and there are infinitely many for which is infinite dimensional.
Moreover, we characterize inductive limits of sequences of separable Banach
spaces which support a hypercyclic operator.Comment: The paper is submitted to Journal of LM
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