Geodesic
Hypercyclicity of special operators on Hilbert function spaces
Czechoslovak Mathematical Journal, Tome 57 (2007) no. 3, pp. 1035-1041 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

In this paper we give some sufficient conditions for the adjoint of a weighted composition operator on a Hilbert space of analytic functions to be hypercyclic.
In this paper we give some sufficient conditions for the adjoint of a weighted composition operator on a Hilbert space of analytic functions to be hypercyclic.
Classification : 30H05, 47A16, 47B33, 47B37
Keywords: multiplier; orbit; hypercyclic vector; multiplication operator; weighted composition operator 
@article{CMJ_2007_57_3_a18,
     author = {Yousefi, B. and Haghkhah, S.},
     title = {Hypercyclicity of special operators on {Hilbert} function spaces},
     journal = {Czechoslovak Mathematical Journal},
     pages = {1035--1041},
     year = {2007},
     volume = {57},
     number = {3},
     mrnumber = {2356938},
     zbl = {1174.47312},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2007_57_3_a18/}
}
TY  - JOUR
AU  - Yousefi, B.
AU  - Haghkhah, S.
TI  - Hypercyclicity of special operators on Hilbert function spaces
JO  - Czechoslovak Mathematical Journal
PY  - 2007
SP  - 1035
EP  - 1041
VL  - 57
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/CMJ_2007_57_3_a18/
LA  - en
ID  - CMJ_2007_57_3_a18
ER  - 
%0 Journal Article
%A Yousefi, B.
%A Haghkhah, S.
%T Hypercyclicity of special operators on Hilbert function spaces
%J Czechoslovak Mathematical Journal
%D 2007
%P 1035-1041
%V 57
%N 3
%U http://geodesic.mathdoc.fr/item/CMJ_2007_57_3_a18/
%G en
%F CMJ_2007_57_3_a18
Yousefi, B.; Haghkhah, S. Hypercyclicity of special operators on Hilbert function spaces. Czechoslovak Mathematical Journal, Tome 57 (2007) no. 3, pp. 1035-1041. http://geodesic.mathdoc.fr/item/CMJ_2007_57_3_a18/

[1] J.  Bes: Three problems on hypercyclic operators. PhD. Thesis, Kent State University, 1998.

[2] J.  Bes, A. Peris: Hereditarily hypercyclic operators. J.  Funct. Anal. 167 (1999), 94–112. | DOI | MR

[3] P. S. Bourdon: Orbits of hyponormal operators. Mich. Math. J. 44 (1997), 345–353. | DOI | MR | Zbl

[4] P. S. Bourdon, J. H.  Shapiro: Cyclic Phenomena for Composition Operators. Memoirs of the Am. Math. Soc.  125. Am. Math. Soc., Providence, 1997. | MR

[5] P. S.  Bourdon, J.  H.  Shapiro: Hypercyclic operators that commute with the Bergman backward shift. Trans. Am. Math. Soc 352 (2000), 5293–5316. | DOI | MR

[6] R. M.  Gethner, J. H. Shapiro: Universal vectors for operators on spaces of holomorphic functions. Proc. Am. Math. Soc. 100 (1987), 281–288. | DOI | MR

[7] G.  Godefroy, J. H.  Shapiro: Operators with dense, invariant cyclic vector manifolds. J. Funct. Anal. 98 (1991), 229–269. | DOI | MR

[8] K.  Goswin, G.  Erdmann: Universal families and hypercyclic operators. Bull. Am. Math. Soc. 35 (1999), 345–381. | MR

[9] D. A. Herrero: Limits of hypercyclic and supercyclic operators. J. Funct. Anal. 99 (1991), 179–190. | DOI | MR | Zbl

[10] C.  Kitai: Invariant closed sets for linear operators. Thesis, University of Toronto, Toronto, 1982.

[11] C. Read: The invariant subspace problem for a class of Banach spaces. 2. Hypercyclic operators. Isr. J.  Math. 63 (1988), 1–40. | DOI | MR

[12] S.  Rolewicz: On orbits of elements. Stud. Math. 32 (1969), 17–22. | DOI | MR | Zbl

[13] H. N.  Salas: Hypercyclic weighted shifts. Trans. Am. Math. Soc. 347 (1995), 993–1004. | DOI | MR | Zbl

[14] A. L.  Shields, L. J.  Wallen: The commutants of certain Hilbert space operators. Indiana Univ. Math. J. 20 (1971), 777–788. | DOI | MR

[15] B.  Yousefi, H.  Rezaei: Hypercyclicity on the algebra of Hilbert-Schmidt operators. Result. Math. 46 (2004), 174–180. | DOI | MR

[16] B.  Yousefi, H.  Rezaei: Some necessary and sufficient conditions for Hypercyclicity Criterion. Proc. Indian Acad. Sci. (Math. Sci.) 115 (2005), 209–216. | DOI | MR