Jordan structures in Banach spaces
The author revisits the proof of the following result by \textit{W. Kaup} [Math. Appl., Dordr. 303, 204--214 (1994; Zbl 0810.46075)]: A bounded symmetric domain in a complex Banach space is biholomorphically equivalent to the open unit ball of a \(JB^*\)-triple. A \(JB^*\)-triple is a complex Banach space with a Jordan triple product and an involution satisfying some conditions. Further, the author gives some applications of \(JB^*\)-triples. One of them is as follows: A linear bijection \(\varphi \) between \(JB^*\)-triples is an isometry if and only if \(\varphi \) is a triple homomorphism, that is, \(\varphi \) preserves the triple product NEWLINE\[NEWLINE\varphi (\{a,b,c\})=\{\varphi (a),\varphi (b),\varphi (c)\}.NEWLINE\]
scientific article; zbMATH DE number 6082492