Fredholm composition operators on spaces of holomorphic functions
Fredholm composition operators on spaces of holomorphic functions
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DOI：
10.1007/bf01192459
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发表时间：
1994-06
影响因子：
0.8
通讯作者：
O. Hatori
中科院分区：
文献类型：
--
作者：
O. Hatori
研究了全纯函数向量空间上的复合算子。给出了算子值域具有有限余维数的必要条件。作为结果的一个推论，证明了在具有C ~ 2边界的严格伪凸域、多圆盘、紧有边Riemann曲面或有界域D上的全纯函数的Banach空间上的复合算子C φ可逆当且仅当它是Fredholm算子当且仅当φ是全纯自同构.
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 operatorCφon a certain Banach space of holomorphic functions on a strictly pseudoconvex domain withC2boundary or a polydisc or a compact bordered Riemann surface or a bounded domainDsuch that intD = Dis invertible if and only if it is a Fredholm operator if and only if φ is a holomorphic automorphism.