The Schwarz inequality in Archimedean \(f\)-algebras. (English) Zbl 0861.46002
Summary: It is shown in an elementary, intrinsic way that a positive definite quadratic polynomial in an Archimedean \(f\)-algebra has a negative discriminant. As a corollary, a Schwarz inequality is obtained for positive linear mapping between Archimedean \(f\)-algebras, both real and complex.
MSC:
| 46A40 | Ordered topological linear spaces, vector lattices |
Keywords:
positive definite quadratic polynomial; Archimedean \(f\)-algebra; negative discriminant; Schwarz inequalityReferences:
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