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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On boundedness of composition operators on $H^{2}(B_{2})$
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by Joseph A. Cima, Charles S. Stanton and Warren R. Wogen PDF
Proc. Amer. Math. Soc. 91 (1984), 217-222 Request permission

Abstract:

Composition operators on the Hardy space ${H^2}$ of the ball in ${C^2}$ are studied. Some sufficient conditions are given for a composition operator to be bounded. A class of inner mappings is given which induces isometric composition operators. Another class of inner mappings is shown to induce unbounded composition operators.
References
  • Barbara D. MacCluer, Iterates of holomorphic self-maps of the unit ball in $\textbf {C}^{N}$, Michigan Math. J. 30 (1983), no.Β 1, 97–106. MR 694933, DOI 10.1307/mmj/1029002792
  • β€”, Spectra of compact composition operators on ${H^P}\left ( {{B_N}} \right )$, preprint.
  • Eric A. Nordgren, Composition operators on Hilbert spaces, Hilbert space operators (Proc. Conf., Calif. State Univ., Long Beach, Calif., 1977) Lecture Notes in Math., vol. 693, Springer, Berlin, 1978, pp.Β 37–63. MR 526531
  • Walter Rudin, Function theory in the unit ball of $\textbf {C}^{n}$, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 241, Springer-Verlag, New York-Berlin, 1980. MR 601594
  • Walter Rudin, Inner functions in the unit ball of $\textbf {C}^{n}$, J. Functional Analysis 50 (1983), no.Β 1, 100–126. MR 690001, DOI 10.1016/0022-1236(83)90062-9
  • R. K. Singh and S. D. Sharma, Composition operators and several complex variables, Bull. Austral. Math. Soc. 23 (1981), no.Β 2, 237–247. MR 617066, DOI 10.1017/S0004972700007097
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Additional Information
  • © Copyright 1984 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 91 (1984), 217-222
  • MSC: Primary 47B37; Secondary 32A35
  • DOI: https://doi.org/10.1090/S0002-9939-1984-0740174-7
  • MathSciNet review: 740174