K-theory for commutants in the Calkin algebra

K-Homology, Assembly and Rigidity Theorems for Relative Eta Invariants

“…This is an approach that was originally suggested by Paschke [31], and then developed by the authors in [19] and [21]. To this end, let us consider a Hilbert space H that is equipped with a representation of the C * -algebra C(X) as bounded operators.…”

A remark on the Kasparov groups Exti(A, B)

“…(iv) Proposition 3 was proved by Paschke [8] in the case B -C (up to a minor point: Paschke has to assume the homotopy-invariance property for Ext 0 A. We do not have to make this assumption, because Kasparov has proved the homotopy-invariance of Ext in full generality for A separable, B with a strictly positive element).…”

“…We do not have to make this assumption, because Kasparov has proved the homotopy-invariance of Ext in full generality for A separable, B with a strictly positive element). Paschke uses his result to construct a part of the Pimsner-Voiculescu exact sequence for the Extgroups of the crossed product of a C*-algebra by an automorphism ( [8], Theorem 7). Paschke's reasoning can be generalized with little effort: PROPOSITION …”

A short proof of an index theorem

“…Combining these maps with the Paschke-Valette-Skandalis duality map [29,28,19,26] from K 0 (Q) to Ext(C, C 0 (M )), we have the diagram…”