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Sur la topologie du groupe des automorphismes analytiques d’un domaine cerclé borné. (French) Zbl 0546.32012
The following result is proved: let D be a bounded circular domain in a complex Banach space E and let G(D) be the group of analytic automorphisms of D. Then the local uniform convergence topology on G(D) coincides with the uniform convergence topology; in particular, if $$E={\mathbb{C}}^ n$$, the compact-open topology on G(D) coincides with the uniform convergence topology.
Reviewer: G.Roos

##### MSC:
 32M05 Complex Lie groups, group actions on complex spaces 32M15 Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (complex-analytic aspects) 54A10 Several topologies on one set (change of topology, comparison of topologies, lattices of topologies) 46G20 Infinite-dimensional holomorphy 32K05 Banach analytic manifolds and spaces