In , Martínez-Avendaño and Zatarain-Vera  proved that hypercyclic coanalytic Toeplitz operators are subspace-hypercyclic under certain conditions. particular that the operator is universal in the sense of Glasner and Weiss) admits frequently hypercyclic vectors with irregularly visiting orbits. where is an operator with dense generalised kernel, must lie in the norm closure of the hypercyclic operators on, in fact in the closure of the.
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Hypercyclic operator – Wikipedia
Functional analysis Operator hyoercyclic Invariant subspaces.
The yypercyclic is a special case of broader notions of topological transitivity see topological mixingand universality. Such an x is then called hypercyclic vector. Home Questions Tags Users Unanswered.
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In other words, the smallest closed invariant subset containing x is the whole space. The proof seems correct to me. Sign up using Facebook. Email Required, but never shown.
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In mathematicsespecially functional analysisa hypercyclic operator on a Banach space X is a bounded linear operator T: Universality in general involves a set of mappings from one topological space to another instead of a sequence of powers of a single operator mapping from X to Xbut has a similar meaning to hypercyclicity. This is material I’m self studying. Sign up using Email and Password.
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