Factorization of mappings and general existence theorems in locally convex spaces (Q2462252)

This article present several extensions of Grothendieck's homomorphism theorem for continuous linear maps between locally convex spaces. These results imply a necessary and sufficient condition for a Lipschitz map between Fréchet spaces to be bijective with an inverse which is also Lipschitz. Another consequence of the results presented here was used by G. Zampieri to prove that semiglobal smooth solvability for overdetermined systems with constant coefficients implies global smooth solvability. An excellent presentation of Grothendieck's homomorphism theorem can be found in Chapter~32 of [\textit{G.\,Köthe}, ``Topological Vector Spaces.\ II'' (Grundlehren 237; New York etc.:\ Springer) (1979; Zbl 0417.46001)]. A useful surjectivity criterion for continuous linear operators between Fréchet spaces was given in Theorem 26.1 of [\textit{R.\,Meise} and \textit{D.\,Vogt}, ``Introduction to Functional Analysis'' (Oxford Graduate Texts in Mathematics 2; Oxford:\ Clarendon Press) (1997; Zbl 0924.46002)]. It has been used successfully in applications to complex analysis and linear partial differential operators.