HYPERCYCLIC OPERATORS PDF
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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 Operators approximable by hypercyclic operators
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. Post as a guest Name. Functional analysis Operator theory Invariant subspaces.
However, it was not until the s when hypercyclic operators started to be more intensively studied. There is no hypercyclic operator in finite-dimensional spaces, but the property of hypercyclicity in spaces of infinite dimension is not a rare phenomenon: 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.
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The hypercyclicity is a special case of broader notions of topological transitivity see topological mixingand universality. Thank you I’ve changed it.
This is material I’m self studying. Views Read Edit View history. In other words, the smallest closed invariant subset containing x is the whole space.
 Frequently hypercyclic operators with irregularly visiting orbits
Sign up using Email and Password. In mathematicsespecially functional analysisa hypercyclic operator operatlrs a Banach space X is a bounded linear operator T: Sign up using Facebook.
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