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Hypercyclic operators on non-locally convex spaces
Author(s):
Jochen
Wengenroth
Journal:
Proc. Amer. Math. Soc.
131
(2003),
1759-1761.
MSC (2000):
Primary 47A16, 46A16
Posted:
January 15, 2003
MathSciNet review:
1955262
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Abstract:
We transfer a number of fundamental results about hypercyclic operators on locally convex spaces (due to Ansari, Bès, Bourdon, Costakis, Feldman, and Peris) to the non-locally convex situation. This answers a problem posed by A. Peris [Multi-hypercyclic operators are hypercyclic, Math. Z. 236 (2001), 779-786].
References:
-
- 1.
- S.I. Ansari, Hypercyclic and cyclic vectors, J. Funct. Anal. 128 (1995), 374-383. MR 96h:47002
- 2.
- J.P. Bès, Invariant manifolds of hypercyclic vectors for the real scalar case, Proc. Amer. Math. Soc. 127 (1999), 1801-1804. MR 99i:47002
- 3.
- P. Bourdon, Invariant manifolds of hypercyclic vectors, Proc. Amer. Math. Soc. 118 (1993), 845-847. MR 93i:47002
- 4.
- P.S. Bourdon and N.S. Feldman, Somewhere dense orbits are everywhere dense, preprint, Washington and Lee University, 2001.
- 5.
- G. Costakis, On a conjecture of D. Herrero concerning hypercyclic operators, C. R. Acad. Sci. Paris Ser. I Math. 130 (2000), 179-182. MR 2001a:47012
- 6.
- K.G. Große-Erdmann, Universal families and hypercyclic operators, Bull. Amer. Math. Soc. 36 (1999), 345-381. MR 2000c:47001
- 7.
- D.A. Herrero, Hypercyclic operators and chaos, J. Operator Theory 28 (1992), 93-103. MR 95g:47031
- 8.
- A. Peris, Multi-hypercyclic operators are hypercyclic, Math. Z. 236 (2001), 779-786. MR 2002a:47008
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Additional Information:
Jochen
Wengenroth
Affiliation:
FB IV -- Mathematik, Universität Trier, D -- 54286 Trier, Germany
Email:
wengen@uni-trier.de
DOI:
10.1090/S0002-9939-03-07003-5
PII:
S 0002-9939(03)07003-5
Keywords:
Hypercyclic operators,
supercyclic operators,
multi-hypercyclic operators
Received by editor(s):
November 23, 2001
Posted:
January 15, 2003
Additional Notes:
The author is indebted to Alfredo Peris for several very helpful remarks on a former version of this note.
Communicated by:
Jonathan M. Borwein
Copyright of article:
Copyright
2003,
American Mathematical Society
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