Full paper in PDF:
$%J. M. Isidro and L. Stachó, Pointwise convergent nets of holomorphic automorphisms of the unit
ball of Cartan factors, Rev. Mat. Univ. Complut. Madrid 8 (1995), no. 1, 71–90.%$
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
jmisidro@zmat.usc.es | Bolyai Intézete
Aradi Vértanuk tere 1
6720 Szeged — Hungary |
| |
Received: July 14, 1993
Revised: May 3, 1994
ABSTRACT
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.