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Compact elements and smallest faithful representation of $ C\sp *$-algebras

Authors: Raphael A. Hauser and Heinrich Matzinger
Journal: Proc. Amer. Math. Soc. 123 (1995), 3379-3384
MSC: Primary 46L05; Secondary 47B10
MathSciNet review: 1285995
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Abstract: Let A be a $ {C^ \ast }$-algebra which either allows a faithful separable representation or is postliminal. We prove that A then admits a smallest faithful representation if and only if the ideal of compact elements is an essential ideal in A.

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