Atomic decomposition of real JBW\(^*\)-triples (Q2716949)
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scientific article; zbMATH DE number 1599659
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Atomic decomposition of real JBW\(^*\)-triples |
scientific article; zbMATH DE number 1599659 |
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16 May 2001
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atomic decomposition
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real \(\text{JB}^*\)-triple
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real \(\text{JBW}^*\)-triple
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\(w^*\)-closed ideals
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Cartan factors
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atomic part
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socle
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annihilator
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0.85162115
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0.84864604
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0.84734774
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0.8473073
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0.84700584
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Atomic decomposition of real JBW\(^*\)-triples (English)
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A real \(\text{JB}^*\)-triple is a closed real subtriple of a (complex) \(\text{JB}^*\)-triple, and a real \(\text{JBW}^*\)-triple is a real \(\text{JB}^*\)-triple the canonical hermitification of which is a (complex) \(\text{JBW}^*\)-triple. In the complex case, \(\text{JBW}^*\)-triples split into the direct sum of two \(w^*\)-closed ideals, one of them is free of atoms and the other (the \(w^*\)-closed linear hull of all atoms) is a direct sum of a family of Cartan factors. In the present paper the authors provide an analogue of this decomposition for real \(\text{JBW}^*\)-triples.NEWLINENEWLINENEWLINEReviewer's remark: Actually, the atomic part of any (real or complex) \(\text{JBW}^*\)-triple coincides with the \(w^*\)-closure of its socle, and the non-atomic part is precisely the annihilator of the socle.
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