Fredholm composition operators on spaces of holomorphic functions
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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 199146J15 47A53
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