Abstract
We will show that ann×n matrix of continuous linear functionals on a locallyC*-algebraA, which satisfies the generalized positivity condition induces a continuous *-representation ofA on a Hilbert space. This generalizes the classical GNS-representation. Also, we give a necessary and sufficient condition such that this representation is irreducible, and determine a certain class of extreme points in the set of all continuous completely positive linear maps fromA toM n (ℂ) that preserve identity.
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References
Bhatt S. J., Karia D. J.,Complete positivity and C*-nuclearity for inverse limits of C*-algebras, Proc. Indian Acad. Sci. (Math. Sci.),101 (1991), 149–167.
Fragoulopoulou M.,An introduction to the representation theory of topological *-algebras, Schriftenreihe, Univ. Münster,48 (1988), 1–81.
Kaplan A.,Multi-states on C*-algebras, Proc. Amer. Math. Soc.,106 (1989), 437–446.
Phillips N. C.,Inverse limits of C*-algebras, J. Operator Theory,19 (1988), 159–195.
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Joiţa, M. Multi-positive linear functionals on locallyC*-algebras. Rend. Circ. Mat. Palermo 53, 185–194 (2004). https://doi.org/10.1007/BF02872870
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DOI: https://doi.org/10.1007/BF02872870