We show that the entire cyclic cohomology of Banach algebras
defined by Connes has the simplicial normalization property.
A key tool in the proof is the notion and properties of supertraces
on the Cuntz algebra QA. As an example of further applications
of this technique we give a proof of the homotopy invariance of
entire cyclic cohomology.
This paper has appeared in K-theory, volume 9, 1995, pages 353-377.