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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I have no more commnets. 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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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 bypercyclic to these policies. From Wikipedia, the free encyclopedia. This is material I’m self studying.

Oeprators 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.

[] Operators approximable by hypercyclic operators

By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. In other words, the smallest closed invariant subset containing x is the whole space.

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However, it was not until the s when hypercyclic operators started to be more intensively studied. Sign up using Facebook.

Hypercyclic operator

There is no hypercyclic operator in finite-dimensional spaces, but the property of hypercyclicity in spaces of infinite dimension is hypeecyclic a rare phenomenon: 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.

Functional analysis Operator theory Invariant subspaces. The proof seems correct to me. Such an x is then called hypercyclic vector.