Frequent hypercyclicity, chaos, and unconditional Schauder decompositions

Published 9 May 2010 in math.FA | (1005.1416v2)

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.

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