In , Martínez-Avendaño and Zatarain-Vera [10] 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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The proof seems correct to me. From Wikipedia, the free encyclopedia.

Such an x is then called hypercyclic vector. Functional analysis Operator theory Invariant subspaces.

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This page was last edited on 1 Novemberat Sign up using Facebook. There is no hypercyclic operator in finite-dimensional spaces, but the property of hypercyclicity in spaces of infinite dimension is not a rare phenomenon: By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. Views Read Edit View history.

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However, it was not until the s when hypercyclic operators started to be more intensively studied. In mathematicsespecially functional analysisa hypercyclic operator on a Banach space X is a bounded linear operator T: 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.

Mathematics Stack Exchange works best with JavaScript enabled. The hypercyclicity is a special case of broader notions of topological transitivity see topological mixingand universality.

I have no more commnets. Retrieved from ” https: Post as a guest Name. By using this site, you agree to the Terms operarors Use and Privacy Policy. This is material I’m self studying.

Hypercyclic operator – Wikipedia

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Sign up using Email and Password. In other words, the smallest closed invariant subset containing x is the whole space. Universality in general involves a set of mappings from one topological space to another instead of a sequence of powers olerators a single operator mapping from X to Xbut has a similar meaning to hypercyclicity.

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