Common hypercyclic vectors

2009 ◽  
pp. 164-194
Author(s):  
Frederic Bayart ◽  
Etienne Matheron
Keyword(s):  
Hypercyclic Vectors

scholarly journals Algebras of frequently hypercyclic vectors

2020 ◽  
Vol 293 (6) ◽  
pp. 1120-1135 ◽  
Author(s):  
Javier Falcó ◽  
Karl‐G. Grosse‐Erdmann
Keyword(s):  
Hypercyclic Vectors

scholarly journals Remarks on common hypercyclic vectors

2010 ◽  
Vol 258 (1) ◽  
pp. 132-160 ◽  
Author(s):  
Stanislav Shkarin
Keyword(s):  
Hypercyclic Vectors

scholarly journals An Extension of Hypercyclicity forN-Linear Operators

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Juan Bès ◽  
J. Alberto Conejero
Keyword(s):  
Difference Equations ◽  
Entire Functions ◽  
Linear Operators ◽  
Fréchet Space ◽  
Infinite Dimensional ◽  
Bilinear Operators ◽  
Hypercyclic Vectors ◽  
Countable Product ◽  
Dense Orbits ◽  
Residual Sets

Grosse-Erdmann and Kim recently introduced the notion of bihypercyclicity for studying the existence of dense orbits under bilinear operators. We propose an alternative notion of orbit forN-linear operators that is inspired by difference equations. Under this new notion, every separable infinite dimensional Fréchet space supports supercyclicN-linear operators, for eachN≥2. Indeed, the nonnormable spaces of entire functions and the countable product of lines supportN-linear operators with residual sets of hypercyclic vectors, forN=2.

scholarly journals Algebrability of the set of hypercyclic vectors for backward shift operators

2020 ◽  
Vol 366 ◽  
pp. 107082 ◽  
Author(s):  
Javier Falcó ◽  
Karl-G. Grosse-Erdmann
Keyword(s):  
Shift Operators ◽  
Hypercyclic Vectors ◽  
Backward Shift
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