Locally convex quasi \(^*\)-algebras with sufficiently many \(^*\)-representations (Q663669)
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scientific article; zbMATH DE number 6009627
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Locally convex quasi \(^*\)-algebras with sufficiently many \(^*\)-representations |
scientific article; zbMATH DE number 6009627 |
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Locally convex quasi \(^*\)-algebras with sufficiently many \(^*\)-representations (English)
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27 February 2012
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The aim of the authors in this paper is to obtain conditions under which a locally convex quasi \(^*\)-algebra has sufficiently many continuous \(^*\)-representations in an algebra of unbounded operators acting on a Hilbert space to separate its points. They present such conditions which are related to positivity. The results lead to the study of so-called fully representable locally convex quasi \(^*\)-algebras. The authors give several examples of such algebras and study their structure in which the concept of order bounded elements plays a crucial role.
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quasi \(^*\)-algebra
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representable linear functional
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fully representable quasi \(^*\)-algebra
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bounded element
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