Previous |  Up |  Next

Article

Keywords:
hypercyclicity; supercyclicity; cyclicity; weighted composition operators
Summary:
In this paper, we discuss the hypercyclicity, supercyclicity and cyclicity of the adjoint of a weighted composition operator on a Hilbert space of analytic functions.
References:
[1] Bayart, F., Matheron, E.: Dynamics of Linear Operators. Cambridge Tracts in Mathematics 179. Cambridge University Press Cambridge (2009). MR 2533318
[2] Bourdon, P. S., Shapiro, J. H.: Cyclic Phenomena for Composition Operators. Mem. Am. Math. Soc. 596 (1997). MR 1396955 | Zbl 0996.47032
[3] Bourdon, P. S., Shapiro, J. H.: Hypercyclic operators that commute with the Bergman backward shift. Trans. Am. Math. Soc. 352 (2000), 5293-5316. DOI 10.1090/S0002-9947-00-02648-9 | MR 1778507 | Zbl 0960.47003
[4] Cowen, C. C., MacCluer, B. D.: Composition Operators on Spaces of Analytic Functions. Studies in Advanced Mathematics. CRC Press Boca Raton (1995). MR 1397026
[5] Feldman, N. S., Miller, V. G., Miller, T. L.: Hypercyclic and supercyclic cohyponormal operators. Acta Sci. Math. 68 (2002), 303-328. MR 1916583 | Zbl 0997.47004
[6] Forelli, F.: The isometries of $H^{p}$. Can. J. Math. 16 (1964), 721-728. DOI 10.4153/CJM-1964-068-3 | MR 0169081
[7] Gethner, R. M., Shapiro, J. H.: Universal vectors for operators on spaces of holomorphic functions. Proc. Am. Math. Soc. 100 (1987), 281-288. DOI 10.1090/S0002-9939-1987-0884467-4 | MR 0884467 | Zbl 0618.30031
[8] Godefroy, G., Shapiro, J. H.: Operators with dense, invariant, cyclic vector manifolds. J. Funct. Anal. 98 (1991), 229-269. DOI 10.1016/0022-1236(91)90078-J | MR 1111569 | Zbl 0732.47016
[9] Kitai, C.: Invariant closed sets for linear operators. Thesis Univ. of Toronto Toronto (1982). MR 2632793
[10] Rolewicz, S.: On orbits of elements. Stud. Math. 32 (1969), 17-22. MR 0241956 | Zbl 0174.44203
[11] Salas, H. N.: Hypercyclic weighted shifts. Trans. Am. Math. Soc. 347 (1995), 993-1004. DOI 10.1090/S0002-9947-1995-1249890-6 | MR 1249890 | Zbl 0822.47030
[12] Salas, H. N.: Supercyclicity and weighted shifts. Stud. Math. 135 (1999), 55-74. MR 1686371 | Zbl 0940.47005
[13] Shapiro, J. H.: Composition Operators and Classical Function Theory. Tracts in Mathematics. Springer New York (1993). MR 1237406
[14] Yousefi, B., Haghkhah, S.: Hypercyclicity of special operators on Hilbert function spaces. Czech. Math. J. 57 (2007), 1035-1041. DOI 10.1007/s10587-007-0093-1 | MR 2356938 | Zbl 1174.47312
[15] Yousefi, B., Rezaei, H.: Hypercyclic property of weighted composition operators. Proc. Am. Math. Soc. 135 (2007), 3263-3271. DOI 10.1090/S0002-9939-07-08833-8 | MR 2322758 | Zbl 1129.47010
Partner of
EuDML logo