Homological characteristics of operator algebras (Q1819333)
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scientific article; zbMATH DE number 3992205
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Homological characteristics of operator algebras |
scientific article; zbMATH DE number 3992205 |
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Homological characteristics of operator algebras (English)
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1986
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A Banach algebra is called hereditary if every of its closed left ideals is a projective \(A\)-module. For functional algebras \(C(\Omega)\) A. Ya. Khelemski has proved a characterization as algebras with hereditary paracompact spectrum. In the paper under review two results are proved: 1) Separable \(C^*\)-algebras are all hereditary. 2) Infinite dimensional von Neumann algebras are not hereditary.
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projective A-module
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functional algebras
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algebras with hereditary paracompact spectrum
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