Common hypercyclic vectors for the unitary orbit of a hypercyclic operator

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2011.08.056 ◽

2012 ◽

Vol 387 (1) ◽

pp. 17-23 ◽

Author(s):

Kit C. Chan ◽

Rebecca Sanders

Keyword(s):

Hypercyclic Operator ◽

Hypercyclic Vectors ◽

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Common hypercyclic vectors for the conjugate class of a hypercyclic operator

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2010.08.018 ◽

2011 ◽

Vol 375 (1) ◽

pp. 139-148 ◽

Author(s):

Kit C. Chan ◽

Rebecca Sanders

Keyword(s):

Hypercyclic Operator ◽

Conjugate Class ◽

Hypercyclic Vectors

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On chaotic $C_0$-semigroups and infinitely regular hypercyclic vectors

Proceedings of the American Mathematical Society ◽

10.1090/s0002-9939-06-08391-2 ◽

2006 ◽

Vol 134 (10) ◽

pp. 2997-3002 ◽

Author(s):

T. Kalmes

Keyword(s):

Hypercyclic Vectors

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On the set of hypercyclic vectors for the differentiation operator

Israel Journal of Mathematics ◽

10.1007/s11856-010-0104-z ◽

2010 ◽

Vol 180 (1) ◽

pp. 271-283 ◽

Author(s):

Stanislav Shkarin

Keyword(s):

Differentiation Operator ◽

Hypercyclic Vectors

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The semigroup generated by a unitary orbit of a singular matrix

Linear and Multilinear Algebra ◽

10.1080/03081080500423833 ◽

2007 ◽

Vol 55 (5) ◽

pp. 417-428 ◽

Author(s):

H. Radjavi ◽

A. R. Sourour

Keyword(s):

Singular Matrix ◽

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Common hypercyclic vectors for families of backward shift operators

Journal of Operator Theory ◽

10.7900/jot.2015jun13.2106 ◽

2017 ◽

Vol 77 (1) ◽

pp. 3-17

Author(s):

N. Tsirivas

Keyword(s):

Shift Operators ◽

Hypercyclic Vectors ◽

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Common hypercyclic vectors

Dynamics of Linear Operators ◽

10.1017/cbo9780511581113.008 ◽

2009 ◽

pp. 164-194

Author(s):

Frederic Bayart ◽

Etienne Matheron

Keyword(s):

Hypercyclic Vectors

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Algebras of frequently hypercyclic vectors

Mathematische Nachrichten ◽

10.1002/mana.201900184 ◽

2020 ◽

Vol 293 (6) ◽

pp. 1120-1135 ◽

Author(s):

Javier Falcó ◽

Karl‐G. Grosse‐Erdmann

Keyword(s):

Hypercyclic Vectors

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Remarks on common hypercyclic vectors

Journal of Functional Analysis ◽

10.1016/j.jfa.2009.06.032 ◽

2010 ◽

Vol 258 (1) ◽

pp. 132-160 ◽

Author(s):

Stanislav Shkarin

Keyword(s):

Hypercyclic Vectors

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HYPERCYCLIC OPERATOR WEIGHTED SHIFTS

Bulletin of the Korean Mathematical Society ◽

10.4134/bkms.2004.41.4.589 ◽

2004 ◽

Vol 41 (4) ◽

pp. 589-598 ◽

Author(s):

Munmun Hazarika ◽

S.C. Arora

Keyword(s):

Hypercyclic Operator ◽

Weighted Shifts

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An Extension of Hypercyclicity forN-Linear Operators

Abstract and Applied Analysis ◽

10.1155/2014/609873 ◽

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 ◽

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.

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