$KK$-groups definitions

Question

In $K$ Theory of Operator Algebras, page 144 and a paper by Skandalis, page 35 the $KK$ groups are defined differently:

Both are triples $(E,\phi, F)$ but Skandalis does not require the condition that

$$\pi(a)(F-F^*) \in \mathcal{K}(E)$$

Are the definitions different?

Answer 1

I believe they are equivalent, as given in a paper by Kasparov and Skandalis.