Archiv der Mathematik

, Volume 67, Issue 4, pp 312–318 | Cite as

On the Bergman space norm of the Cesàro operator

  • Aristomenis G. Siskakis
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References

  1. [1]
    A. Brown, P. R. Halmos andA. L. Shields, Cesàro operators. Acta Sci. Math.26, 125–137 (1965).Google Scholar
  2. [2]
    C. C. Cowen, Subnormality of the Cesàro operator and a semigroup of composition operators. Indiana Univ. Math. J.33, 305–318 (1984).Google Scholar
  3. [3]
    J. A. Deddens, Analytic Toeplitz and composition operators. Canad. J. Math.24, 859–865 (1972).Google Scholar
  4. [4]
    N.Dunford and J. T.Schwartz, Linear operators I. New York 1988.Google Scholar
  5. [5]
    M. Gonzalez, The fine spectrum of the Cesàro operator in ℓp (1<p<∞). Arch. Math.44, 355–358 (1985).Google Scholar
  6. [6]
    H. Kamowitz, The spectra of composition operators onH p. J. Funct. Anal.18, 132–150 (1975).Google Scholar
  7. [7]
    J. Miao, The Cesàro operator is bounded onH p for 0<p<1. Proc. Amer. Math. Soc.116, 1077–1079 (1992).Google Scholar
  8. [8]
    A.Pazy, Semigroups of linear operators and applications to partial differential equations, Berlin-Heidelberg-New York 1983.Google Scholar
  9. [9]
    J. B. Reade, On the spectrum of the Cesàro operator. Bull. London Math. Soc.17, 263–267 (1985).Google Scholar
  10. [10]
    J. H.Shapiro, Composition operators and classical function theory, Berlin-Heidelberg-New York 1993.Google Scholar
  11. [11]
    A. G. Siskakis, Composition semigroups and the Cesàro operator onH p. J. London Math. Soc. (2)36, 153–164 (1987).Google Scholar
  12. [12]
    A. G. Siskakis, Semigroups of composition operators in Bergman spaces. Bull. Austral. Math. Soc.35, 397–406 (1987).Google Scholar
  13. [13]
    A. G. Siskakis, The Cesàro operator is bounded onH 1. Proc. Amer. Math. Soc.110, 461–462 (1990).Google Scholar
  14. [14]
    K.Zhu, Operator theory on function spaces. Pure Appl. Math.139, New York 1990.Google Scholar

Copyright information

© Birkhäuser Verlag 1996

Authors and Affiliations

  • Aristomenis G. Siskakis
    • 1
  1. 1.Department of MathematicsUniversity of ThessalonikiThessalonikiGreece

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