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Invariant manifolds of hypercyclic vectors for the real scalar case
Author(s):
Juan
P.
Bès
Journal:
Proc. Amer. Math. Soc.
127
(1999),
1801-1804.
MSC (1991):
Primary 47A15, 47A99
Posted:
February 18, 1999
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Abstract:
We show that every hypercyclic operator on a real locally convex vector space admits a dense invariant linear manifold of hypercyclic vectors.
References:
- 1.
- S. I. Ansari, Existence of Hypercyclic Operators on Topological Vector Spaces, J. Funct. Anal. 148 (1997), no. 2, 384-390. CMP 98:01
- 2.
- S. I. Ansari, Hypercyclic and Cyclic Vectors, J. Funct. Anal. 128 (2) (1995). MR 96h:47002
- 3.
- B. Beauzamy, An operator on a separable Hilbert space with all polynomials hypercyclic, Studia Math. T. XCVI (1990), 81-90. MR 91d:47004
- 4.
- P. Bourdon, Invariant Manifolds of Hypercyclic Vectors, Proc. Amer. Math. Soc. 118 (3) (1993), 845-847. MR 93i:47002
- 5.
- G. Godefroy and Joel H. Shapiro, Operators with Dense, Invariant, Cyclic Vector Manifolds, J. Funct. Anal. 98 (1991), 229-269. MR 92d:47029
- 6.
- Domingo A.Herrero, Limits of Hypercyclic and Supercyclic Operators, J. Funct. Anal. 99 (1991), 179-190. MR 92g:47026
- 7.
- C. Kitai, Invariant Closed Sets for Linear Operators, Thesis, University of Toronto (1982).
- 8.
- S. Rolewicz, On orbits of elements, Studia Math. T. XXXII (1969), 17-22. MR 39:3292
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Additional Information:
Juan
P.
Bès
Affiliation:
Department of Mathematics and Computer Science, Kent State University, Kent, Ohio 44242
Address at time of publication:
Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, Ohio 43403
Email:
jbes@mcs.kent.edu, jbes@math.bgsu.edu
DOI:
10.1090/S0002-9939-99-04720-6
PII:
S 0002-9939(99)04720-6
Received by editor(s):
September 17, 1997
Posted:
February 18, 1999
Additional Notes:
The author wishes to thank the support of the Center for International and Comparative Programms and the Graduate Student Senate of Kent State University.
Communicated by:
Theodore W. Gamelin
Copyright of article:
Copyright
1999,
American Mathematical Society
Forward Citation(s): Information for authors on submitting citations The following works have cited this article Krzysztof Jarosz, Hypercyclic Differentiation Operators, Function Spaces (Southern Illinois University at Edwardsville, May 19-23, 1998), Contemp. Math., vol. 232, American Mathematical Society, 1999, pp. 39-46.
K.-G. Grosse-Erdmann, Universal families and hypercyclic operators, Bull. Amer. Math. Soc. (3) 36 (1999), 345-381.
L. Bernal-Gonzalez, Densely hereditarily hypercyclic sequences and large hypercyclic manifolds, Proc. Amer. Math. Soc. 127 (1999), 3279-3285.
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