Frequent hypercyclicity,chaos, and unconditional Schauder decompositions |
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| Authors: | Manuel De la Rosa Leonhard Frerick Sophie Grivaux Alfredo Peris |
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| Institution: | 1.Institut Universitari de Matemàtica Pura i Aplicada (IUMPA),Universitat Politècnica de València,València,Spain;2.FB IV Mathematik,Universit?t Trier,Trier,Germany;3.Laboratoire Paul Painlevé, UMR 8524,Université Lille 1 Cité Scientifique,Villeneuve d’Ascq Cedex,France;4.IUMPA Department de Matemàtica Aplicada, edifici 7A,Universitat Politècnica de València,València,Spain |
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| 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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