Available in electronic format
Available in print format
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
     

Composition operators: Hyperinvariant subspaces, quasi-normals and isometries

Author(s): Bruce A. Cload
Journal: Proc. Amer. Math. Soc. 127 (1999), 1697-1703.
MSC (1991): Primary 47B38; Secondary 47A15, 47B06, 47B20
Posted: February 11, 1999
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: We exhibit hyperinvariant subspaces of some composition operators. We also consider quasi-normal composition operators and discuss the commutant of isometric composition operators.


References:

1.
P.S. Bourdon, Convergence of the Koenigs' Sequence, preprint.

2.
P.S. Bourdon & J. Shapiro, Mean Growth of Koenigs' Eigenfunctions, J. Amer. Math. Soc. 10 (1997), 299-325. MR 97h:30040
3.
P.S. Bourdon & J. Shapiro, Riesz Composition Operators, Preprint.

4.
A. Brown, On a Class of Operators, Proc. Amer. Math. Soc. 4, 723-728. MR 15:538c

5.
R.B. Burckel, Iterating Analytic Self-Maps of Discs, Amer. Math. Monthly 88(1981), 396-407. MR 82g:30046

6.
B. Cload, Generating the Commutant of a Composition Operator, Cont. Math. 239 (1998), 11-15.

7.
B. Cload, Toeplitz Operators in the Commutant of a Composition Operator, to appear in Studia Math.

8.
J.B. Conway, Subnormal Operators, Boston: Pitman Adv. Pub. Program, 1981. MR 83i:47030

9.
C.C. Cowen, Commuting Analytic Functions, Trans. Amer. Math. Soc. 265(1981), 69-95. MR 85i:30054

10.
C.C. Cowen & B. MacCluer, Composition Operators on Spaces of Analytic Functions, CRC Press, 1995. MR 97i:47056

11.
H. Dowson, Spectral Theory of Linear Operators, Academic Press, 1978 MR 80c:47022

12.
P.R. Halmos, Shifts on Hilbert Spaces, J, Reine Angew. Math., 208(1961), 102-112. MR 27:2868

13.
E.A. Nordgren, Composition Operators, Canadian J. Math. 20(1968), 442-449. MR 36:6961

14.
P. Poggi-Corradini, Hardy Norm Convergence of the Koenigs' sequence for non-univalent maps, preprint.

15.
P. Poggi-Corradini, The Hardy Class of Koenigs maps, preprint.

16.
H. Radjavi & P. Rosenthal, Invariant Subspaces, Springer-Verlag (1973). MR 51:3924

17.
H. Schwarz, Composition Operators on $H^p$, Ph.D. Thesis, University of Toledo, 1969.

18.
J.H. Shapiro, Composition Operators and Classical Function Theory, Springer-Verlag, New York, 1993. MR 94k:47049

19.
T.T. West, The Decomposition of Riesz Operators, Proc. London Math. Soc. 3(1966), 131-140. MR 33:6417


Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 47B38, 47A15, 47B06, 47B20

Retrieve articles in all Journals with MSC (1991): 47B38, 47A15, 47B06, 47B20


Additional Information:

Bruce A. Cload
Affiliation: Department of Mathematics, Brock University, St. Catharines, Ontario, Canada L2S 3A1
Email: bcload@spartan.ac.brocku.ca

DOI: 10.1090/S0002-9939-99-04663-8
PII: S 0002-9939(99)04663-8
Received by editor(s): May 13, 1997
Received by editor(s) in revised form: September 8, 1997
Posted: February 11, 1999
Additional Notes: The results in this paper are part of the author's doctoral thesis under the direction of Peter Rosenthal at the University of Toronto. The author would like to thank NSERC for their support as well as the referee for his kind comments and helpful suggestions.
Communicated by: Theodore W. Gamelin
Copyright of article: Copyright 1999, American Mathematical Society


  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2009, American Mathematical Society
Privacy Statement
Search the AMSPowered by Google