Frequent hypercyclicity, chaos, and unconditional Schauder decompositions

Details Frequent hypercyclicity, chaos, and unconditional Schauder decompositions Frequent hypercyclicity, chaos, and unconditional Schauder decompositions

2010-05-09

arxiv.org/abs/1005.1416v2

Mathematics

Functional Analysis

9 pages, to appear in Israel J. Math

Scientific paper

We prove that if X is any complex separable infinite-dimensional Banach space
with an unconditional Schauder decomposition, X supports an operator T which is
chaotic and frequently hypercyclic. In contrast with the complex case, we
observe that there are real Banach spaces with an unconditional basis which
support no chaotic operator.

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