Abstract:
Let G be a countable exact discrete group. G has the strong
invariant approximation property(SIAP) if and only if
C
∗
u
(G, S)
G = C
∗
λ
(G) ⊗ S
for any Hilbert space H and closed subspace S ⊆ H. We shall use results
of Haagerup and Kraus on the approximation property (AP) to investigate
some permanence properties of the SIAP for discrete groups. This can be done
most efficiently for exact groups. In this paper we describe that the stability
properties of the SIAP property pass to semi direct products, and extensions
for discrete exact groups.
