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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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From Wikipedia, the free encyclopedia. Such an x is then called hypercyclic vector. Sign up using Facebook.

Hypercyclic operator – Wikipedia

I have no more commnets. Sign up or log in Sign up using Google. 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: Email Required, but never shown. 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.


[] Operators approximable by hypercyclic operators

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By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. Mathematics Stack Exchange works best with JavaScript enabled. Sign up using Email and Password. The hypercyclicity is a special case of broader notions of topological transitivity see topological mixingand universality.

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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 hypefcyclic X is a bounded linear operator T: In other words, the smallest closed invariant subset containing x is the whole space.

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This is material I’m self studying. 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. By using this site, you agree to the Terms of Use and Privacy Policy. Post Your Answer Discard By hypercycljc “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 hyperfyclic subject to these policies.

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