On the unitary equivalence of close \(C^ *\)-algebras (Q1081085)
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scientific article; zbMATH DE number 3969406
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the unitary equivalence of close \(C^ *\)-algebras |
scientific article; zbMATH DE number 3969406 |
Statements
On the unitary equivalence of close \(C^ *\)-algebras (English)
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1984
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Let A be a \(C^*\)-algebra which is either commutative or separable unital with a continuous trace. Suppose D and D' are subalgebras of a common \(C^*\)-algebra and D is an extension of A by the compacts. It is shown that if the Hausdorff distance between their unit balls is sufficiently small, then D and D' are unitarily equivalent.
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perturbation
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continuous trace
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extension
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Hausdorff distance
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unitarily equivalent
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