On absorbing extensions

Thomsen, Klaus

doi:10.1090/S0002-9939-00-05936-0

On absorbing extensions
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Proc. Amer. Math. Soc. 129 (2001), 1409-1417 Request permission

Abstract:

Building on the work of Kasparov we show that there always exists a trivial absorbing extension of $A$ by $B \otimes \mathcal K$, provided only that $A$ and $B$ are separable. If $A$ is unital there is a unital trivial extension which is unitally absorbing.

References

William Arveson, Notes on extensions of $C^{^*}$-algebras, Duke Math. J. 44 (1977), no. 2, 329–355. MR 438137
Bruce Blackadar, $K$-theory for operator algebras, Mathematical Sciences Research Institute Publications, vol. 5, Springer-Verlag, New York, 1986. MR 859867, DOI 10.1007/978-1-4613-9572-0
Nigel Higson, $C^*$-algebra extension theory and duality, J. Funct. Anal. 129 (1995), no. 2, 349–363. MR 1327182, DOI 10.1006/jfan.1995.1054
G. G. Kasparov, Hilbert $C^{\ast }$-modules: theorems of Stinespring and Voiculescu, J. Operator Theory 4 (1980), no. 1, 133–150. MR 587371
Kjeld Knudsen Jensen and Klaus Thomsen, Elements of $KK$-theory, Mathematics: Theory & Applications, Birkhäuser Boston, Inc., Boston, MA, 1991. MR 1124848, DOI 10.1007/978-1-4612-0449-7
William L. Paschke, $K$-theory for commutants in the Calkin algebra, Pacific J. Math. 95 (1981), no. 2, 427–434. MR 632196
Georges Skandalis, Une notion de nucléarité en $K$-théorie (d’après J. Cuntz), $K$-Theory 1 (1988), no. 6, 549–573 (French, with English summary). MR 953916, DOI 10.1007/BF00533786
Alain Valette, A remark on the Kasparov groups $\textrm {Ext}(A,\,B)$, Pacific J. Math. 109 (1983), no. 1, 247–255. MR 716300