Book Review
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MathSciNet review:
1568159
Full text of review:
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Book Information:
Author:
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:
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.
[1] P. S. Bourdon and J. S. Shapiro, Cyclic properties of composition operators (to appear).
Carl C. Cowen, Composition operators on Hilbert spaces of analytic functions: a status report, Operator theory: operator algebras and applications, Part 1 (Durham, NH, 1988) Proc. Sympos. Pure Math., vol. 51, Amer. Math. Soc., Providence, RI, 1990, pp. 131–145. MR 1077383, DOI 10.1016/j.jpaa.2009.05.015
James Guyker, On reducing subspaces of composition operators, Acta Sci. Math. (Szeged) 53 (1989), no. 3-4, 369–376. MR 1033609
Valentin Matache, On the minimal invariant subspaces of the hyperbolic composition operator, Proc. Amer. Math. Soc. 119 (1993), no. 3, 837–841. MR 1152988, DOI 10.1090/S0002-9939-1993-1152988-8
Barbara D. MacCluer and Joel H. Shapiro, Angular derivatives and compact composition operators on the Hardy and Bergman spaces, Canad. J. Math. 38 (1986), no. 4, 878–906. MR 854144, DOI 10.4153/CJM-1986-043-4
Rolf Nevanlinna, Analytic functions, Die Grundlehren der mathematischen Wissenschaften, Band 162, Springer-Verlag, New York-Berlin, 1970. Translated from the second German edition by Phillip Emig. MR 0279280
Eric A. Nordgren, Composition operators, Canadian J. Math. 20 (1968), 442–449. MR 223914, DOI 10.4153/CJM-1968-040-4
[8] -, Composition operators in Hilbert spaces, Hilbert Space Operators, Lecture Notes in Math., vol. 693, Springer-Verlag, Berlin, 1978, pp. 37-63.
Eric Nordgren, Peter Rosenthal, and F. S. Wintrobe, Invertible composition operators on $H^p$, J. Funct. Anal. 73 (1987), no. 2, 324–344. MR 899654, DOI 10.1016/0022-1236(87)90071-1
Eric A. Nordgren, Peter Rosenthal, and F. S. Wintrobe, Composition operators and the invariant subspace problem, C. R. Math. Rep. Acad. Sci. Canada 6 (1984), no. 5, 279–283. MR 764103
Donald Sarason, Angular derivatives via Hilbert space, Complex Variables Theory Appl. 10 (1988), no. 1, 1–10. MR 946094, DOI 10.1080/17476938808814282
[12] H. J. Schwartz, Composition operators on 
, Thesis, Univ. of Toledo, 1968.
Joel H. Shapiro, The essential norm of a composition operator, Ann. of Math. (2) 125 (1987), no. 2, 375–404. MR 881273, DOI 10.2307/1971314
[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.
Warren R. Wogen, Composition operators acting on spaces of holomorphic functions on domains in $\textbf {C}^n$, Operator theory: operator algebras and applications, Part 2 (Durham, NH, 1988) Proc. Sympos. Pure Math., vol. 51, Amer. Math. Soc., Providence, RI, 1990, pp. 361–366. MR 1077457, DOI 10.1090/pspum/051.2/1077457
- [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)
Review Information:
Reviewer:
Peter Rosenthal
Journal:
Bull. Amer. Math. Soc.
32 (1995), 150-153
DOI:
https://doi.org/10.1090/S0273-0979-1995-00562-8
