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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### Hypercyclic operator – Wikipedia

From Wikipedia, the free encyclopedia. Post Your Answer Discard By clicking “Post Your Answer”, you acknowledge that you have read our updated terms of serviceprivacy policy and cookie policyand that your continued use of the website is subject to these policies.

Functional analysis Operator hyoercyclic Invariant subspaces.

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 this site, you agree to the Terms of Use and Privacy Policy. I’m pretty new to this area of study so if there are hyperchclic lacune in my proof I’m sure there are many please let me know.

## Hypercyclic operator

By clicking “Post Your Answer”, you acknowledge that you have read our updated terms of serviceprivacy policy and cookie policyoperator that your continued use of the website is subject to these policies. This page was last edited on 1 Novemberat However, it was not until the s when hypercyclic operators started to be more intensively studied.

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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