On Hilbert modules over locally \(C^*\)-algebras (Q2762841)
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scientific article; zbMATH DE number 1689551
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On Hilbert modules over locally \(C^*\)-algebras |
scientific article; zbMATH DE number 1689551 |
Statements
13 January 2002
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Hilbert modules
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locally \(C^*\)-algebras
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Cauchy-Schwarz inequality
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extension theorem
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strictly positive elements
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On Hilbert modules over locally \(C^*\)-algebras (English)
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There are proved some properties for Hilbert modules over local \(C^*\)-algebras, namely: a simple form of Cauchy-Schwarz inequality, an extension theorem for isomorphisms between local \(C^*\)-algebras to isomorphisms between multiplier algebras, and a stabilization theorem for countably bounded generated Hilbert modules over local \(C^*\)-algebras that generalizes a previous result of \textit{N. C.~Phillips} [J. Operator Theory 19, No. 1, 159-195 (1988; Zbl 0662.46063)]. The technique of strictly positive elements is used and some of their properties in Hilbert modules over local \(C^*\)-algebras are obtained.
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