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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Sign up using Facebook. Thank you I’ve changed it. Post as a guest Name. The proof seems correct to me. There is no hypercyclic operator in finite-dimensional spaces, but the property of hypercyclicity in spaces of infinite dimension is not a rare phenomenon: Such an x is then called hypercyclic vector. Sign up using Email and Password. Retrieved from ” https: This page was last edited opedators 1 Novemberat Functional analysis Operator theory Invariant subspaces.
Hypercyclic operator – Wikipedia
This is material I’m self studying. The hypercyclicity is a special case of broader notions of topological transitivity see topological mixingand universality. Email Required, but never shown.
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I’m pretty new to this area of study so if there are logical lacune in my proof I’m sure there are many please let me know. 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.