Frequent hypercyclicity, chaos, and unconditional Schauder decompositions
arXiv:1005.1416
Abstract
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.
9 pages, to appear in Israel J. Math