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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:
- [1]
- P. S. Bourdon and J. S. Shapiro, Cyclic properties of composition operators.
- [2]
- C. C. Cowen, \emph{Composition operators on Hilbert spaces of analytic functions\,\RM : A status report}, Amer. Math. Soc., Providence, RI, 1990 pp.~131--145.
- [3]
- J. Guyker, On reducing subspaces of composition operators, Acta Sci. Math. (Szeged) \textbf{53} (1989), 369--376.
- [4]
- V. Matache, On the minimal invariant subspaces of the hyperbolic composition operator, Proc. Amer. Math. Soc. \textbf{119} (1993), 837--841.
- [5]
- B. D. MacCluer and J. S. Shapiro, Angular derivatives and compact composition operators on the Hardy and Bergman spaces, Canad. J. Math. \textbf{38} (1986), 878--906.
- [6]
- R. Nevanlinna, Analytic functions, Springer-Verlag, New York, 1970.
- [7]
- E. A. Nordgren, Composition operators, Canad. J. Math. \textbf{20} (1968), 442--449.
- [8]
- E. A. Nordgren, \emph{Composition operators in Hilbert spaces}, Springer-Verlag, Berlin, 1978 pp.~37--63.
- [9]
- E. A. Nordgren, P. Rosenthal, F. Wintrobe, Invertible composition operators on $\Scr H^2$, J. Funct. Anal. \textbf{73} (1987), 324--344.
- [10]
- E. A. Nordgren, P. Rosenthal, F. Wintrobe, Composition operators and the invariant subspace problem, C. R. Math. Rep. Acad. Sci. Canada \textbf{6} (1984), 279--282.
- [11]
- D. Sarason, Angular derivatives via Hilbert space, Complex Variables Theory Appl. \textbf{10} (1988), 1--10.
- [12]
- H. J. Schwartz, Composition operators on $\Scr H^2$, Thesis, Univ. of Toledo, 1968.
- [13]
- J. H. Shapiro, The essential norm of a composition operator, Ann. of Math. (2) \textbf{125} (1987), 375--404.
- [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) \textbf{55} (1931), 105--128.
- [16]
- W. Wogen, \emph{Composition operators acting on spaces of holomorphic functions on domains in $\Bbb C^n$}, Part II, Amer. Math. Soc., Providence, RI, 1990 pp.~361--366.
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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