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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Topologically mixing hypercyclic operators


Authors: George Costakis and Martín Sambarino
Journal: Proc. Amer. Math. Soc. 132 (2004), 385-389
MSC (2000): Primary 47A16, 47B37; Secondary 37B05
Published electronically: June 10, 2003
MathSciNet review: 2022360
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Abstract: Let $X$ be a separable Fréchet space. We prove that a linear operator $T:X\to X$ satisfying a special case of the Hypercyclicity Criterion is topologically mixing, i.e. for any given open sets $U,V$ there exists a positive integer $N$ such that $T^n(U)\cap V\neq \emptyset$ for any $n\ge N.$ We also characterize those weighted backward shift operators that are topologically mixing.


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Additional Information

George Costakis
Affiliation: Department of Mathematics, University of Maryland, College Park, Maryland 20742
Address at time of publication: Vitinis 25 N. Philadelphia, Athens, Greece
Email: geokos@math.umd.edu

Martín Sambarino
Affiliation: Department of Mathematics, University of Maryland, College Park, Maryland 20742
Address at time of publication: IMERL, Fac. Ingenieria, University de la República, CC30 Montevideo, Uruguay
Email: samba@fing.edu.uy

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07016-3
PII: S 0002-9939(03)07016-3
Keywords: Hypercyclic operators, hypercyclicity criterion, topologically mixing
Received by editor(s): May 13, 2002
Received by editor(s) in revised form: September 18, 2002
Published electronically: June 10, 2003
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2003 American Mathematical Society