A sufficient condition for \(\text{Proj}^1\chi=0\)
Given a countable projective spectrum \({\mathcal X}=(X_k)\) of topological vector spaces, \textit{V. P. Palamodov} [Mat. Sb. (N.S.) 75(117), 567-603 (1968; Zbl 0175.41801)] introduced a functor \(\text{Proj}^1{\mathcal X}\). For the case where each \(X_k\) is an inductive limit of Banach spaces (with some compatibility condition), the authors prove a sufficient condition for \(\text{Proj}^1{\mathcal X}=0\) [see also \textit{L. Frerick} and \textit{J. Wengenroth}, Arch. Math. 67, No. 4, 296-301 (1996; Zbl 0859.46046)]. If the \(X_k\) are DFS-spaces, this condition is shown to be necessary as well. Applications to partial differential operators are sketched.
scientific article; zbMATH DE number 1046973