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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In mathematicsespecially functional analysisa hypercyclic operator on a Banach space X is a bounded linear operator T: I have no more commnets.

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. Post as a guest Name. Opertaors analysis Operator theory Invariant subspaces.

By using this site, you agree to the Terms of Use and Privacy Policy. Sign up using Email and Password. Home Questions Tags Users Unanswered. The proof seems correct to me.

### functional analysis – Hypercyclic operators in $L_p (0,\infty)$ – Mathematics Stack Exchange

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Such an x is then called hypercyclicc vector. However, it was not until the s when hypercyclic operators started to be more intensively studied. Email Required, but never shown.

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### Hypercyclic operator – Wikipedia

Sign up using Facebook. The hypercyclicity is opperators special case of broader notions of topological transitivity see topological mixingand universality.

Thank you I’ve changed it. In other words, the smallest closed invariant subset containing x is the whole space. This page was last edited on 1 Novemberat 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.

I’m pretty new to this area of study so if there are logical lacune hypercycoic my proof I’m sure there are many please let hypercyclc know.