Jordan structures in Banach spaces (Q2912204)
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scientific article; zbMATH DE number 6082492
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Jordan structures in Banach spaces |
scientific article; zbMATH DE number 6082492 |
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Jordan structures in Banach spaces (English)
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14 September 2012
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Jordan triple system
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bounded symmetric domain
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\(JB^*\)-triple
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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\[NEWLINE\varphi (\{a,b,c\})=\{\varphi (a),\varphi (b),\varphi (c)\}.NEWLINE\]
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