Abstract:
Analytic properties of invariant approximation property, studies analytic tech niques from operator theory that encapsulate geometric properties of a group.
We show that the following theorem holds: For a discrete group G satisfying the
rapid decay property with respect to a conditionally negative length function `,
the reduced C
∗
-algebra C
∗
r (G) has the invariant approximation property. We
then use this to show that some groups have invariant approximation property.
We also show that if G is a free product group satisfying the rapid decay prop erty with respect to a conditionally negative length function `, then the reduced
C
∗
-algebra C
∗
r (G) has the invariant approximation property.
