A sufficient condition for vanishing of the derived projective limit functor
In 1968, V. P. Palamodov developed the theory of the projective limit functor in the category of locally convex spaces and introduced the derived projective limit functor Proj\(^1\) as a tool for investigating surjectivity problems in various parts of analysis (e.g. solvability of partial differential equations). He and V. S. Retakh obtained a characterization of Proj\(^1=0\) in terms of linear topological properties of the spaces forming the projective spectrum, which has been applied also recently e.g. by R. Braun, R. Meise and D. Vogt to describe surjectivity of convolution operators on classes of ultradifferentiable functions and by Vogt to the splitting theory for Fréchet spaces. For these applications one condition in Palamodov's and Retakh's characterization is very difficult to check. The paper under review contains as the main result a sufficient condition for Proj\(^1=0\) which fits better in the situations mentioned above. Using this new condition a characterization of the splitting relation for large classes of Fréchet spaces is given which completes results of Vogt.
scientific article; zbMATH DE number 938606