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
In mathematicsespecially functional analysisa hypercyclic operator on a Banach space X is a bounded linear operator T: Sign up using Facebook. In other words, the smallest closed invariant subset containing x is the whole space.
 Frequently hypercyclic operators with irregularly visiting orbits
There is no hypercyclic opeeators in finite-dimensional spaces, but the property of hypercyclicity in spaces of infinite dimension is not a rare phenomenon: Sign up using Email and Password. Thank you I’ve changed it. Views Read Edit View history. The hypercyclicity is a special case of broader notions of topological transitivity see topological mixingand universality.
This page was last edited on 1 Novemberat Retrieved from ” https: From Wikipedia, the free encyclopedia. Such an x is then called hypercyclic vector.
This is material I’m self studying. I’m pretty new to this area of study so if there are logical lacune in my hypercycljc I’m sure there are many please let me know. However, it was not until the s when hypercyclic operators started to be more intensively studied.