 
Summary: On the holomorphic rigidity of linear operators
on complex Banach spaces
Jonathan Arazy 1
Department of Mathematics
University of Haifa
Haifa 31905
Israel
jarazy@mathcs2.haifa.ac.il
Wilhelm Kaup 1
Mathematisches Institut
Universitšat Tšubingen
Auf der Morgenstelle 10
D72076 Tšubingen
Germany
kaup@unituebingen.de
ABSTRACT. We study linear operators L: E ! F of norm 1 between complex Banach spaces with
open unit balls B ae E, D ae F that are rigid in the following sense: f = L on B for every holomorphic
mapping f : B ! D with f(0) = 0 and derivative L at the origin 0 2 B. These considerations are
related to the vector valued Schwarz Lemma.
1. Introduction
