A Banach Space which Admits No Chaotic Operator

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Li–Yorke and distributionally chaotic operators (2010, background): “X can be written as T = λI +S, where λ ∈ Cand S is a strictly singular operator. The class of hereditarily indecomposable spaces appeared for the ﬁrst time in relation with hypercyclicityand chaos in [9], where it was provedthat some complex separable Banach spaces admit no Devaney chaotic operator.”
Linear chaos and frequent hypercyclicity (2014, background): “Indeed, there exist separable infinite-dimensional Banach spaces which support no chaotic operator [15] and no frequently hypercyclic operator [34].”
Distributional chaos for backward shifts (2009, background): “This fact contrasts with the existence of infinite dimensional separable Banach spaces without chaotic operators in the sense of Devaney [17].”