Positive linear forms vanish on the radical (Q1977739)
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scientific article; zbMATH DE number 1449083
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Positive linear forms vanish on the radical |
scientific article; zbMATH DE number 1449083 |
Statements
Positive linear forms vanish on the radical (English)
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11 December 2000
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The paper deals with a complex algebra \((A,*)\) with involution \(*\) and a unit. A linear form \(L\) on \(A\) is said to be positive, if \(L(a^*a)\geq 0\) for all \(a\in A\). The main theorem of the paper states that every positive linear form \(L\) vanishes on the Jacobson radical of \(A\).
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complex \(*\)-algebra
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Jacobson radical
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positive linear form
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