HYPERCYCLIC OPERATORS PDF

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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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Sign up using Facebook. Thank you I’ve changed it. Post as a guest Name. 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: Such an x is then called hypercyclic vector. Sign up using Email and Password. Retrieved from ” https: This page was last edited opedators 1 Novemberat Functional analysis Operator theory Invariant subspaces.

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Hypercyclic operator – Wikipedia

In mathematicsespecially functional analysisa hypercyclic operator on a Banach space X is a bounded linear operator T: Home Questions Tags Users Unanswered. Mathematics Stack Exchange works best with JavaScript enabled. From Wikipedia, the free encyclopedia.

This is material I’m self studying. The hypercyclicity is a special case of broader notions of topological transitivity see topological mixingand universality. Email Required, but never shown.

I have no more commnets. However, it was not until the s when hypercyclic operators started to be more intensively studied. Views Read Edit View history. 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.

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In other words, the smallest closed invariant subset containing x is the whole space. By using this site, you agree to the Terms of Use and Privacy Policy.

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Hypercyclic operator

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. 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.

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