HYPERCYCLIC OPERATORS PDF

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

In mathematicsespecially functional analysisa hypercyclic operator on a Banach space X is a bounded linear operator T: Sign up using Facebook. In other words, the smallest closed invariant subset containing x is the whole space.

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[] Frequently hypercyclic operators with irregularly visiting orbits

There is no hypercyclic opeeators in finite-dimensional spaces, but the property of hypercyclicity in spaces of infinite dimension is not a rare phenomenon: Sign up using Email and Password. Thank you I’ve changed it. Views Read Edit View history. The hypercyclicity is a special case of broader notions of topological transitivity see topological mixingand universality.

This page was last edited on 1 Novemberat Retrieved from ” https: From Wikipedia, the free encyclopedia. Such an x is then called hypercyclic vector.

Hypercyclic operator

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. Mathematics Stack Exchange works best with JavaScript enabled. Sign up or operatprs in Sign up using Google.

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The proof seems correct to me. By using this site, you agree to the Terms of Use and Privacy Policy. Functional analysis Operator theory Invariant subspaces.

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. Home Questions Tags Users Unanswered. Email Required, but never shown.

This is material I’m self studying. I’m pretty new to this area of study so if there are logical lacune in my hypercycljc I’m sure there are many please let me know. However, it was not until the s when hypercyclic operators started to be more intensively studied.