SOME NONLINEAR METHODS IN FRECHET OPERATOR RINGS AND PSI-ASTERISK-ALGEBRAS

Two different inverse function theorems, one of Nash-Moser type, the o ther due to H. OMORI, are extended to obtain special surjectivity resu lts in locally convex and locally pseudoconvex Frechet algebras genera ted by group actions and derivations. In particular, the following fac torization problem is discussed. Let Psi be a locally pseudo-convex Fr echel algebra with unit e and T-+:Psi --> Psi a continuous linear oper ator. Does there exist a neighborhood U of 0 such that the equation e - y = (e - T(+)x)(e - T(-)x), where T-- = I-Psi - T, has a solution x is an element of Psi for every y is an element of U?