\(C\)-algebras on some free-Banach spaces (Q1616624)
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scientific article; zbMATH DE number 6974389
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(C\)-algebras on some free-Banach spaces |
scientific article; zbMATH DE number 6974389 |
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\(C\)-algebras on some free-Banach spaces (English)
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7 November 2018
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The article is devoted to non-Archimedean analogs of \(C\)-algebras. Operator algebras on free Banach spaces are considered over a field \(K\). The field \(K\) is with a norm satisfying the strong triangle inequality (non-archimedean norm) having nonnegative values. The residue class field of \(K\) is supposed to be real. Gel'fand transforms of such commutative Banach algebras are studied. Relations with algebras of continuous functions are investigated. Their realizations with the help of spectral measures are considered.
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\(C\)-algebra
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compact operator
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spectral measure
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scalar measure
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integration
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non-Archimedean analysis
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