Geometric characterization of \(L_{1}\)-spaces (Q2866759)
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scientific article; zbMATH DE number 6238585
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Geometric characterization of \(L_{1}\)-spaces |
scientific article; zbMATH DE number 6238585 |
Statements
16 December 2013
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facially symmetric space
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tripotent
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unitary
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\(L_1\)-space
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Geometric characterization of \(L_{1}\)-spaces (English)
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The authors prove that every neutral strongly facially symmetric real space in which every maximal geometric tripotent is unitary, is isometrically isomorphic to an \(L_1(\mu)\)-space. The result is false in the complex case. Examples of neutral complex strongly facially symmetric spaces are the preduals of complex von Neumman algebras and, in this case, the tripotents correspond to partial isometries.
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