Hypercyclicity of weighted convolution operators on homogeneous spaces
HTML articles powered by AMS MathViewer
- by C. Chen and C-H. Chu PDF
- Proc. Amer. Math. Soc. 137 (2009), 2709-2718 Request permission
References
- Shamim I. Ansari, Existence of hypercyclic operators on topological vector spaces, J. Funct. Anal. 148 (1997), no. 2, 384–390. MR 1469346, DOI 10.1006/jfan.1996.3093
- Frédéric Bayart and Sophie Grivaux, Frequently hypercyclic operators, Trans. Amer. Math. Soc. 358 (2006), no. 11, 5083–5117. MR 2231886, DOI 10.1090/S0002-9947-06-04019-0
- Frédéric Bayart and Sophie Grivaux, Invariant Gaussian measures for operators on Banach spaces and linear dynamics, Proc. Lond. Math. Soc. (3) 94 (2007), no. 1, 181–210. MR 2294994, DOI 10.1112/plms/pdl013
- F. Bayart and É. Matheron, Hypercyclic operators failing the hypercyclicity criterion on classical Banach spaces, J. Funct. Anal. 250 (2007), no. 2, 426–441. MR 2352487, DOI 10.1016/j.jfa.2007.05.001
- Teresa Bermúdez, Antonio Bonilla, José A. Conejero, and Alfredo Peris, Hypercyclic, topologically mixing and chaotic semigroups on Banach spaces, Studia Math. 170 (2005), no. 1, 57–75. MR 2142183, DOI 10.4064/sm170-1-3
- Luis Bernal-González, On hypercyclic operators on Banach spaces, Proc. Amer. Math. Soc. 127 (1999), no. 4, 1003–1010. MR 1476119, DOI 10.1090/S0002-9939-99-04657-2
- L. Bernal-González and K.-G. Grosse-Erdmann, The hypercyclicity criterion for sequences of operators, Studia Math. 157 (2003), no. 1, 17–32. MR 1980114, DOI 10.4064/sm157-1-2
- Juan Bès and Alfredo Peris, Hereditarily hypercyclic operators, J. Funct. Anal. 167 (1999), no. 1, 94–112. MR 1710637, DOI 10.1006/jfan.1999.3437 b G.D. Birkhoff, Démonstration d’un théorème élémentaire sur les fonctions entières, C.R. Acad. Sci. Paris 189 (1929) 473-475.
- José Bonet, Hypercyclic and chaotic convolution operators, J. London Math. Soc. (2) 62 (2000), no. 1, 253–262. MR 1772185, DOI 10.1112/S0024610700001174
- José Bonet and Alfredo Peris, Hypercyclic operators on non-normable Fréchet spaces, J. Funct. Anal. 159 (1998), no. 2, 587–595. MR 1658096, DOI 10.1006/jfan.1998.3315
- Jeng-Chung Chen and Sen-Yen Shaw, Topological mixing and hypercyclicity criterion for sequences of operators, Proc. Amer. Math. Soc. 134 (2006), no. 11, 3171–3179. MR 2231900, DOI 10.1090/S0002-9939-06-08308-0
- Cho-Ho Chu, Matrix convolution operators on groups, Lecture Notes in Mathematics, vol. 1956, Springer-Verlag, Berlin, 2008. MR 2450997, DOI 10.1007/978-3-540-69798-5
- George Costakis and Martín Sambarino, Topologically mixing hypercyclic operators, Proc. Amer. Math. Soc. 132 (2004), no. 2, 385–389. MR 2022360, DOI 10.1090/S0002-9939-03-07016-3 DLRR M. De La Rosa and C. Read, A hypercyclic operator whose direct sum $T\oplus T$ is not hypercyclic, J. Operator Theory (to appear).
- R. deLaubenfels and H. Emamirad, Chaos for functions of discrete and continuous weighted shift operators, Ergodic Theory Dynam. Systems 21 (2001), no. 5, 1411–1427. MR 1855839, DOI 10.1017/S0143385701001675
- Wolfgang Desch, Wilhelm Schappacher, and Glenn F. Webb, Hypercyclic and chaotic semigroups of linear operators, Ergodic Theory Dynam. Systems 17 (1997), no. 4, 793–819. MR 1468101, DOI 10.1017/S0143385797084976
- Gerald B. Folland, A course in abstract harmonic analysis, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1995. MR 1397028
- Robert M. Gethner and Joel H. Shapiro, Universal vectors for operators on spaces of holomorphic functions, Proc. Amer. Math. Soc. 100 (1987), no. 2, 281–288. MR 884467, DOI 10.1090/S0002-9939-1987-0884467-4
- Gilles Godefroy and Joel H. Shapiro, Operators with dense, invariant, cyclic vector manifolds, J. Funct. Anal. 98 (1991), no. 2, 229–269. MR 1111569, DOI 10.1016/0022-1236(91)90078-J
- 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
- K.-G. Grosse-Erdmann, Recent developments in hypercyclicity, RACSAM. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. 97 (2003), no. 2, 273–286 (English, with English and Spanish summaries). MR 2068180 kit C. Kitai, Invariant closed sets for linear operators, PhD Thesis, University of Toronto, 1982.
- G. R. MacLane, Sequences of derivatives and normal families, J. Analyse Math. 2 (1952), 72–87 (English, with Hebrew summary). MR 53231, DOI 10.1007/BF02786968
- Alfredo Peris and Luis Saldivia, Syndetically hypercyclic operators, Integral Equations Operator Theory 51 (2005), no. 2, 275–281. MR 2120081, DOI 10.1007/s00020-003-1253-9
- Henrik Petersson, Spaces that admit hypercyclic operators with hypercyclic adjoints, Proc. Amer. Math. Soc. 134 (2006), no. 6, 1671–1676. MR 2204278, DOI 10.1090/S0002-9939-05-08167-0
- S. Rolewicz, On orbits of elements, Studia Math. 32 (1969), 17–22. MR 241956, DOI 10.4064/sm-32-1-17-22
- Héctor N. Salas, Hypercyclic weighted shifts, Trans. Amer. Math. Soc. 347 (1995), no. 3, 993–1004. MR 1249890, DOI 10.1090/S0002-9947-1995-1249890-6
Additional Information
- C. Chen
- Affiliation: School of Mathematical Sciences, Queen Mary, University of London, London E1 4NS, United Kingdom
- Email: c.chen@qmul.ac.uk
- C-H. Chu
- Affiliation: School of Mathematical Sciences, Queen Mary, University of London, London E1 4NS, United Kingdom
- MR Author ID: 199837
- Email: c.chu@qmul.ac.uk
- Received by editor(s): October 28, 2008
- Published electronically: March 10, 2009
- Communicated by: Nigel J. Kalton
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 137 (2009), 2709-2718
- MSC (2000): Primary 47A16, 47B37, 47B38, 43A85, 44A35
- DOI: https://doi.org/10.1090/S0002-9939-09-09889-X
- MathSciNet review: 2497483