Biweights on partial *-algebras

Antoine, Jean-Pierre;Inoue, A.;Trapani, C.
(2000) Journal of Mathematical Analysis and Applications — Vol. 242, n° 2, p. 164-190 (2000)

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Authors
  • Antoine, Jean-Pierreorcid-logoUCLouvain
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  • Inoue, A.
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  • Trapani, C.
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Abstract
Representations of *-algebras are generally obtained by the familiar Gelfand-Naimark-Segal (GNS) construction, starting from a positive Linear functional or even a (quasi-) weight, that is, a functional that may take infinite values. In previous works, we have extended this construction to the case of a partial *-algebra, using invariant positive sesquilinear forms, which play the same role as positive linear functionals for *-algebras. In this paper we extend the construction further. by introducing and studying systematically the notion of biweight on a partial *-algebra. In particular, we characterize, through the associated GNS representation, the so-called approximately admissible biweights (i.e., limits of biweights with a bounded GNS representation). (C) 2000 Academic Press.
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Antoine, J.-P., Inoue, A., & Trapani, C. (2000). Biweights on partial *-algebras. Journal of Mathematical Analysis and Applications, 242(2), 164-190. https://doi.org/10.1006/jmaa.1999.6644 (Original work published 2000)