Complex Borel structure in \(JC\)-algebras (Q1174338)
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scientific article; zbMATH DE number 8522
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Complex Borel structure in \(JC\)-algebras |
scientific article; zbMATH DE number 8522 |
Statements
Complex Borel structure in \(JC\)-algebras (English)
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25 June 1992
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Given a \(JC\)-algebra \(A\), let \(\hat A\) denote the Jordan equivalence classes of the Type I factor representation of \(A\) and \(C^*(A)\) its enveloping \(C^*\)-algebra. The authors investigate the relative behavior of the Mackey-Borel structures of \(\hat A\) and \(C^*(A)\), relating that to primitive ideals, to ideal structure and to enveloping Borel *-algebras. The main result lists a number of conditions equivalent to \(A\) being Borel isomorphic to the self-adjoint part of a \(C^*\)-algebra.
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\(JC\)-algebra
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Jordan equivalence classes
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Type I factor representation
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enveloping \(C^*\)-algebra
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Mackey-Borel structures
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primitive ideals
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ideal structure
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enveloping Borel *-algebras
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self-adjoint part of a \(C^*\)-algebra
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