Partial *-algebras of closable operators. 2. States and representations of partial *-algebras
(1991) Research Institute for Mathematical Sciences. Publications — Vol. 27, n° 3, p. 399-430 (1991)
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- Authors
Antoine, Jean-Pierre 
- Abstract
- This second paper on partial Op*-algebras is devoted to the theory of representations. A new definition of invariant positive sesquilinear forms on partial *-algebras is proposed, which enables to perform the familiar GNS construction. In order to get a better control of the corresponding representations, we introduce and study a restricted class of partial Op*-algebras, called partial GW*-algebras, which turn up naturally in a number of problems. As an example, we extend Powers' results about the standardness of GNS representations of abelian partial *-algebras.
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Citations
Antoine, J.-P., Inoue, A., & Trapani, C. (1991). Partial *-algebras of closable operators. 2. States and representations of partial *-algebras. Research Institute for Mathematical Sciences. Publications, 27(3), 399-430. https://doi.org/10.2977/prims/1195169662 (Original work published 1991)