In , Martínez-Avendaño and Zatarain-Vera  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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There is no hypercyclic operator in finite-dimensional spaces, but the property of hypercyclicity in spaces of infinite dimension is not a rare phenomenon: Functional analysis Operator theory Invariant subspaces.
Universality in general involves a set of mappings from one operahors space to another instead of operatofs sequence of powers of a single operator mapping from X to Xbut has a similar meaning to hypercyclicity.
The hypercyclicity is a special case of broader notions of topological transitivity see topological mixingand universality. Sign up or log in Sign up using Google. Sign up using Facebook. The proof seems correct to me.
Hypercyclic operator – Wikipedia
From Wikipedia, the free encyclopedia. Such an x is then called hypercyclic vector.
Thank you I’ve changed it. In mathematicsespecially functional analysisa hypercyclic operator on a Banach space X is a bounded linear operator T: Retrieved from ” https: Sign up using Email and Password.
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However, it was not until the s when hypercyclic operators started to be more intensively studied. I have no more commnets. Email Required, but never shown. 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. Post as a guest Name.