Integral Equations and Operator Theory

, Volume 18, Issue 2, pp 202–210 | Cite as

Fredholm composition operators on spaces of holomorphic functions

  • Osamu Hatori


Composition operators on vector spaces of holomorphic functions are considered. Necessary conditions that range of the operator is of a finite codimension are given. As a corollary of the result it is shown that a composition operatorCφ on a certain Banach space of holomorphic functions on a strictly pseudoconvex domain withC2 boundary or a polydisc or a compact bordered Riemann surface or a bounded domainD such that intD = D is invertible if and only if it is a Fredholm operator if and only if φ is a holomorphic automorphism.

MSC 1991

46J15 47A53 


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Copyright information

© Birkhäuser Verlag 1994

Authors and Affiliations

  • Osamu Hatori
    • 1
  1. 1.Department of MathematicsTokyo Medical CollegeTokyo 160Japan

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