Relative K-homology and normal operators

Details Relative K-homology and normal operators Relative K-homology and normal operators

2005-05-12

arxiv.org/abs/math/0505250v1

Mathematics

Operator Algebras

24 pages

Scientific paper

Let $A$ be a C*-algebra, $J \subset A$ a C*-subalgebra, and let $B$ be a stable C*-algebra. Under modest assumptions we organize invertible C*-extensions of $A$ by $B$ that are trivial when restricted onto $J$ to become a group $Ext_J^{-1}(A,B)$, which can be computed by a six-term exact sequence which generalizes the excision six-term exact sequence in the first variable of $KK$-theory. Subsequently we investigate the relative K-homology which arises from the group of relative extensions by specializing to abelian C*-algebras. It turns out that this relative K-homology carries substantial information also in the operator theoretic setting from which the BDF theory was developed and we conclude the paper by extracting some of this information on approximation of normal operators.

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