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Hypercyclicity and supercyclicity for invertible bilateral weighted shifts

Author(s): Nathan S. Feldman
Journal: Proc. Amer. Math. Soc. 131 (2003), 479-485.
MSC (2000): Primary 47A16, 47B37
Posted: June 3, 2002
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Abstract: We give a characterization of the invertible bilateral weighted shifts that are hypercyclic or supercyclic. Although there is a general characterization due to H. Salas, in the invertible case the conditions simplify greatly.

References:

1.
P. S. Bourdon and J. H. Shapiro, Cyclic Phenomena for Composition Operators, Memoirs of the AMS, 125, AMS, Providence, RI, 1997. MR 97h:47023

2.
N.S. Feldman, T.L. Miller and V.G. Miller Hypercyclic and Supercyclic Cohyponormal Operators, To appear in Acta. Sci. Math.

3.
R. M. Gethner and J. H. Shapiro, Universal vectors for operators on spaces of holomorphic functions, Proc. AMS, 100 (1987), 281-288. MR 88g:47060

4.
H. M. Hilden and L. J. Wallen, Some cyclic and non-cyclic vectors of certain operators, Ind. Univ. Math. J., 23 (1974), 557-565. MR 48:4796

5.
C. Kitai, Invariant closed sets for linear operators, Dissertation, Univ. of Toronto, 1982.

6.
S. Rolewicz, On orbits of elements, Studia Math., 32 (1969), 17-22. MR 39:3292

7.
H. N. Salas, Hypercyclic weighted shifts, Trans Amer. Math. Soc., 347 (1995), 993-1004. MR 95e:47042

8.
H. N. Salas, Supercyclicity and weighted shifts, Studia Math. 135 (1999), no. 1, 55-74. MR 2000b:47020

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Additional Information:

Nathan S. Feldman
Affiliation: Department of Mathematics, Washington and Lee University, Lexington, Virginia 24450
Email: feldmann@wlu.edu

DOI: 10.1090/S0002-9939-02-06537-1
PII: S 0002-9939(02)06537-1
Keywords: Hypercyclic, supercyclic, bilateral weighted shift
Received by editor(s): April 28, 2001
Received by editor(s) in revised form: September 17, 2001
Posted: June 3, 2002
Communicated by: Joseph A. Ball
Copyright of article: Copyright 2002, American Mathematical Society

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