On \(m\)-convexity of commutative real Waelbroeck algebras (Q2752317)
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scientific article; zbMATH DE number 1660805
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On \(m\)-convexity of commutative real Waelbroeck algebras |
scientific article; zbMATH DE number 1660805 |
Statements
16 October 2001
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\(Q\)-algebra
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\(m\)-convex
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locally convex Fréchet \(Q\)-algebra
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unital topological algebra
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Waelbroeck algebra
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complexification
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0.90025365
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0.8750824
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0.87211347
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On \(m\)-convexity of commutative real Waelbroeck algebras (English)
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A unital topological algebra \(A\) is said to be a \(Q\)-algebra if the set (group) \(G(A)\) of all its invertible elements is open. When \(A\) is a \(Q\)-algebra and the operation of taking an inverse is continuous on \(G(A)\), \(A\) is said to be a Waelbroeck algebra.NEWLINENEWLINENEWLINEThe author's abstract: We prove that the complexification of a commutative real Waelbroeck algebra is again such an algebra, and apply this result for showing that a commutative real locally conves Fréchet \(Q\)-algebra must be \(m\)-convex, and, more generally, a commutative real locally convex Waelbroeck algebra must be \(m\)-convex. In this way we extend onto the real case two results known in the complex case and this solve a problem posed previously.
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