Stability of a bi-additive functional equation in Banach modules over a \(C^\star\)-algebra (Q714285)
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scientific article; zbMATH DE number 6096246
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Stability of a bi-additive functional equation in Banach modules over a \(C^\star\)-algebra |
scientific article; zbMATH DE number 6096246 |
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Stability of a bi-additive functional equation in Banach modules over a \(C^\star\)-algebra (English)
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19 October 2012
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Summary: We solve the bi-additive functional equation \[ f(x + y, z - w) + f(x - y, z + w) = 2f(x, z) - 2f(y, w) \] and prove that every bi-additive Borel function is bilinear. We investigate the stability of a bi-additive functional equation in Banach modules over a unital \(C^\star\)-algebra.
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bi-additive functional equation
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stability
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Banach modules
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\(C^\star\)-algebra
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