A SMOOTHING PROPERTY FOR FRECHET SPACES

A smoothing property (S-Omega)(t) for Frechet spaces is introduced gen eralizing the classical concept of smoothing operators which are impor tant in the proof of Nash-Moser inverse function theorems. For Frechet -Hilbert spaces property (Omega) in standard form in the sense of D. V ogt is shown to be sufficient for (S Omega)(t). For instance, the spac es E(K) of infinitely differentiable functions in the sense of Whitney have property (S-Omega)(t) for an arbitrary compact K subset of R(n); applications to extensions of Whitney functions with estimates are in cluded. In a forthcoming paper, an inverse Function theorem will be pr oved for Frechet spaces with properties (S-Omega)(t) and (DN); this ap plies to E(K) if the compact K = <(K)over circle over bar> subset of R (n) is subanalytic. (C) 1996 Academic Press, Inc.