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Hypercyclic property of weighted composition operators
Author(s):
B.
Yousefi;
H.
Rezaei
Journal:
Proc. Amer. Math. Soc.
135
(2007),
3263-3271.
MSC (2000):
Primary 47B33, 47B38
Posted:
May 14, 2007
MathSciNet review:
2322758
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Additional information
Abstract:
In the present paper we investigate conditions under which a holomorphic self-map of the open unit disk induces a hypercyclic weighted composition operator in the space of holomorphic functions.
References:
-
- 1.
- G. D. Birkhoff, Démonstration d'un théorème élémentaire sur les fonctions entières, C.R. Acad. Sci. Paris 189 (1929), 473-475.
- 2.
- P. S. Bourdon and J. H. Shapiro, Cyclic composition operators on
 , Proc. Symp. Pure Math. 51 Part 2 (1990), 43-53. MR 1077418 (91h:47028) - 3.
- P. S. Bourdon and J. H. Shapiro, Cyclic phenomena for composition operators, Mem. Amer. Math. Soc. 596 (1997).MR 1396955 (97h:47023)
- 4.
- P. S. Bourdon and J. H. Shapiro, The numerical ranges of automorphic composition operators, J. Math. Analysis and Appl. 251 (2000), 839-854.MR 1794773 (2001i:47039)
- 5.
- K. C. Chan and J. H. Shapiro, The cyclic behavior of translation operators on Hilbert spaces of entire functions, Indiana Univ. Math. J. 40 (1991), 1421-1449.MR 1142722 (92m:47060)
- 6.
- J. B. Conway, Function of one complex variable, Springer-Verlag, (1973).MR 0447532 (56:5843)
- 7.
- C. C. Cowen and B. D. MacCluer, Composition operators on spaces of analytic functions, CRC Press, Boca Raton (1995). MR 1397026 (97i:47056)
- 8.
- N. S. Feldman, The dynamics of cohyponormal operators, Contemp. Math. 321, Amer. Math. Soc. (2003), 71-85.MR 1978808 (2004b:47033)
- 9.
- R. M. Gethner and J. H. Shapiro, Universal vectors for operators on spaces of holomorphic functions, Proc. Amer. Math. Soc. 100 (1987), 281-288.MR 0884467 (88g:47060)
- 10.
- G. Godefroy and J. H. Shapiro, Operators with dense invariant cyclic vector manifolds, J. Funct. Anal. 98 (1991), 229-269.MR 1111569 (92d:47029)
- 11.
- C. G. Grosse-Erdmann, Universal families and hypercyclic operators, Bull. Amer. Math. Soc. 36 (1999). MR 1685272 (2000c:47001)
- 12.
- K. G. Grosse-Erdmann, Recent developments in hypercyclicity, Rev. R. Acad. Cien. Serie A. Mat. Vol. 97 (2) (2003), 273-286.MR 2068180 (2005c:47010)
- 13.
- C. Kitai, Invariant closed sets for linear operators, Thesis, Univ. of Toronto, (1982).
- 14.
- F. Leon-Saavedra and V. Muller, Rotations of hypercyclic and supercyclic operators, Integral Equations Operator Theory 50 (2004), 385-391. MR 2104261 (2005g:47009)
- 15.
- S. Rolewicz, On orbits of elements, Studia Math. 32 (1969), 17-22.MR 0241956 (39:3292)
- 16.
- H. N. Salas, Hypercyclic weighted shifts, Trans. Amer. Math. Soc. 347 (1995), 993-1004.MR 1249890 (95e:47042)
- 17.
- J. H. Shapiro, Composition operators and classical function theory, Springer-Verlag, New York, (1993). MR 1237406 (94k:47049)
- 18.
- J. H. Shapiro, Notes on dynamics of linear operators. http://www. math.msu.edu/ shapiro, (2001).
- 19.
- A. Shields and L. Wallen, The commutant of certain Hilbert space operators, Indiana Univ. Math. J. 20 (1971), 777-788.MR 0287352 (44:4558)
- 20.
- B. Yousefi and H. Rezaei, Some necessary and sufficient conditions for Hypercyclicity Criterion, Proc. Indian Acad. Sci. (Math. Sci.), 115 (2) (2005), 209-216. MR 2142466 (2006a:47018)
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Additional Information:
B.
Yousefi
Affiliation:
Department of Mathematics, College of Sciences, Shiraz University, Shiraz 71454, Iran
Email:
byousefi@shirazu.ac.ir
H.
Rezaei
Affiliation:
Department of Mathematics, College of Sciences, Shiraz University, Shiraz 71454, Iran
DOI:
10.1090/S0002-9939-07-08833-8
PII:
S 0002-9939(07)08833-8
Keywords:
Weighted composition operator,
hypercyclic operator,
Denjoy-Wolff point,
Julia-Carath\'eodory theorem,
linear-fractional model theorem,
Schwarz's lemma.
Received by editor(s):
January 26, 2006
Received by editor(s) in revised form:
June 30, 2006
Posted:
May 14, 2007
Additional Notes:
This paper is a part of the second author's doctoral thesis written at Shiraz University under the direction of the first author
Dedicated:
Dedicated to the memory of Professor K. Seddighi
Communicated by:
Joseph A. Ball
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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