Departamento de Análisis Matemático Facultad de Matemáticas 15076 Santiago de Compostela — Spain
jmisidro@zmat.usc.es | Bolyai Intézete Aradi Vértanuk tere 1 6720 Szeged — Hungary |
A classical result due to H. Cartan states that if a sequence of holomorphic automorphisms of the unit disk of is pointwise convergent on to a limit and is bounded away from the boundary , then is a holomorphic automorphism of . The analogous result for the open unit ball of a complex Banach space is not true in general. Here we consider pointwise convergent nets of holomorphic automorphisms of the unit balls of those Banach spaces known as special Cartan factors and establish a sufficient condition for the pointwise limit to be a holomorphic automorphism of .
1991 Mathematics Subject Classification: 46G20, 32M15.