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An abstract Voiculescu-Brown-Douglas-Fillmore absorption theorem. (English) Zbl 1058.46041
The present paper is devoted to a generalization of so called Weyl-von Neumann theorems of Voiculescu, Kasparov, Kirchberg and Lin, which in turn extends a result of L. G. Brown, R. G. Douglas and P. A. Fillmore [Ann. Math. (2) 105, 265–324 (1977; Zbl 0376.46036)]. Namely, an intrinsic characterization is obtained of those extensions of one separable $$C^*$$-algebra by another which are absorbing in a certain natural nuclear sense. If the first algebra (which is assumed to be a stable ideal) or the quotient is nuclear, then this condition reduces to that considered by earlier authors.

##### MSC:
 46L35 Classifications of $$C^*$$-algebras
##### Keywords:
$$C^*$$-algebra; extension; absorption; purely large extension
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