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Book Review
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Book Information
Author(s):
Joel H. Shapiro
Title:
Composition operators and classical function theory
Additional book information:
Universitext: Tracts in Mathematics, Springer-Verlag, New York, 1993, xvi + 223 pp., US$34.00. ISBN 0-387-94067-7
Author(s):
R. K. Singh and J. S. Manhas
Title:
Composition operators on function spaces
Additional book information:
North-Holland Mathematics Studies, vol. 179, North-Holland, Amsterdam, 1993, x+315 pp., 200 Dfl. ISBN 0-444-81593-7.
References:
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- [1]
- P. S. Bourdon and J. S. Shapiro, Cyclic properties of composition operators (to appear).
- [2]
- C. C. Cowen, Composition operators on Hilbert spaces of analytic functions: A status report, Proc. Sympos. Pure Math., vol. 51, Part I, Amer. Math. Soc., Providence, RI, 1990, pp. 131-145. MR 1077383 (91m:47043)
- [3]
- J. Guyker, On reducing subspaces of composition operators, Acta Sci. Math. (Szeged) 53 (1989), 369-376. MR 1033609 (91a:47041)
- [4]
- V. Matache, On the minimal invariant subspaces of the hyperbolic composition operator, Proc. Amer. Math. Soc. 119 (1993), 837-841. MR 1152988 (93m:47038)
- [5]
- B. D. MacCluer and J. S. Shapiro, Angular derivatives and compact composition operators on the Hardy and Bergman spaces, Canad. J. Math. 38 (1986), 878-906. MR 854144 (87h:47048)
- [6]
- R. Nevanlinna, Analytic functions, Springer-Verlag, New York, 1970. MR 0279280 (43:5003)
- [7]
- E. A. Nordgren, Composition operators, Canad. J. Math. 20 (1968), 442-449. MR 0223914 (36:6961)
- [8]
- -, Composition operators in Hilbert spaces, Hilbert Space Operators, Lecture Notes in Math., vol. 693, Springer-Verlag, Berlin, 1978, pp. 37-63.
- [9]
- E. A. Nordgren, P. Rosenthal, F. Wintrobe, Invertible composition operators on
 , J. Funct. Anal. 73 (1987), 324-344. MR 899654 (89c:47044) - [10]
- -, Composition operators and the invariant subspace problem, C. R. Math. Rep. Acad. Sci. Canada 6 (1984), 279-282. MR 764103
- [11]
- D. Sarason, Angular derivatives via Hilbert space, Complex Variables Theory Appl. 10 (1988), 1-10. MR 946094 (89f:30045)
- [12]
- H. J. Schwartz, Composition operators on
 , Thesis, Univ. of Toledo, 1968. - [13]
- J. H. Shapiro, The essential norm of a composition operator, Ann. of Math. (2) 125 (1987), 375-404. MR 881273 (88c:47058)
- [14]
- R. K. Singh, Composition operators, Thesis, Univ. of New Hampshire, 1972.
- [15]
- G. Valiron, Sur l'iteration des fonctions holomorphes dans un demi-plan, Bull. Sci. Math. (2) 55 (1931), 105-128.
- [16]
- W. Wogen, Composition operators acting on spaces of holomorphic functions on domains in
 , Proc. Sympos. Pure Math., vol. 51, Part II, Amer. Math. Soc., Providence, RI, 1990, pp. 361-366. MR 1077457 (91k:47069)
Additional Information:
Reviewer(s):
Peter
Rosenthal
Review Information:
Journal:
Bull. Amer. Math. Soc.
32
(1995),
150-153.
DOI:
10.1090/S0273-0979-1995-00562-8
PII:
S 0273-0979(1995)00562-8
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