Full paper in PDF:
$%J. M. Isidro and L. Stachó, Pointwise convergent nets of holomorphic automorphisms of the unit ball of Cartan factors, Rev. Mat. Univ. Complut. Madrid 8 (1995), no. 1, 7190.%$

Pointwise Convergent Nets of Holomorphic Automorphisms of the Unit Ball of Cartan Factors
José M. ISIDRO and László STACHÓ
Departamento de Análisis Matemático
Facultad de Matemáticas
15076 Santiago de Compostela Spain
Bolyai Intézete
Aradi Vértanuk tere 1
6720 Szeged Hungary

Received: July 14, 1993
Revised: May 3, 1994

A classical result due to H. Cartan states that if a sequence (hn)  of holomorphic automorphisms of the unit disk D  of C  is pointwise convergent on D  to a limit h  and (hn(0))  is bounded away from the boundary @(D)  , then h  is a holomorphic automorphism of D  . The analogous result for the open unit ball D  of a complex Banach space E  is not true in general. Here we consider pointwise convergent nets (hi)  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 h= limi hi  to be a holomorphic automorphism of D  .

1991 Mathematics Subject Classification: 46G20, 32M15.