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.