Hypercyclic operators on non-locally convex spaces

Wengenroth, Jochen

doi:10.1090/S0002-9939-03-07003-5

Hypercyclic operators on non-locally convex spaces
HTML articles powered by AMS MathViewer

by Jochen Wengenroth

Proc. Amer. Math. Soc. 131 (2003), 1759-1761

DOI: https://doi.org/10.1090/S0002-9939-03-07003-5

Published electronically: January 15, 2003

PDF | Request permission

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

Shamim I. Ansari, Hypercyclic and cyclic vectors, J. Funct. Anal. 128 (1995), no. 2, 374–383. MR 1319961, DOI 10.1006/jfan.1995.1036
Juan P. Bès, Invariant manifolds of hypercyclic vectors for the real scalar case, Proc. Amer. Math. Soc. 127 (1999), no. 6, 1801–1804. MR 1485460, DOI 10.1090/S0002-9939-99-04720-6
Paul S. Bourdon, Invariant manifolds of hypercyclic vectors, Proc. Amer. Math. Soc. 118 (1993), no. 3, 845–847. MR 1148021, DOI 10.1090/S0002-9939-1993-1148021-4
P.S. Bourdon and N.S. Feldman, Somewhere dense orbits are everywhere dense, preprint, Washington and Lee University, 2001.
George Costakis, On a conjecture of D. Herrero concerning hypercyclic operators, C. R. Acad. Sci. Paris Sér. I Math. 330 (2000), no. 3, 179–182 (English, with English and French summaries). MR 1748304, DOI 10.1016/S0764-4442(00)00126-9
Karl-Goswin Grosse-Erdmann, Universal families and hypercyclic operators, Bull. Amer. Math. Soc. (N.S.) 36 (1999), no. 3, 345–381. MR 1685272, DOI 10.1090/S0273-0979-99-00788-0
Domingo A. Herrero, Hypercyclic operators and chaos, J. Operator Theory 28 (1992), no. 1, 93–103. MR 1259918
Alfredo Peris, Multi-hypercyclic operators are hypercyclic, Math. Z. 236 (2001), no. 4, 779–786. MR 1827503, DOI 10.1007/PL00004850