Geodesic
Acyclic inductive spectra of Fréchet spaces
Studia Mathematica, Tome 120 (1996) no. 3, pp. 247-258

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We provide new characterizations of acyclic inductive spectra of Fréchet spaces which improve the classical theorem of Palamodov and Retakh. It turns out that acyclicity, sequential retractivity (defined by Floret) and further strong regularity conditions (introduced e.g. by Bierstedt and Meise) are all equivalent. This solves a problem that was folklore since around 1970. For inductive limits of Fréchet-Montel spaces we obtain even stronger results, in particular, Grothendieck's problem whether regular (LF)-spaces are complete has a positive solution in this case and we show that even the weakest regularity conditions already imply acyclicity. One of the main benefits from our results is an improvement in the theory of projective spectra of (DFM)-spaces. We prove the missing implication in a theorem of Vogt and thus obtain evaluable conditions for vanishing of the derived projective limit functor which have direct applications to classical problems of analysis like surjectivity of partial differential operators on various classes of ultradifferentiable functions (as was explained e.g. by Braun, Meise and Vogt).
DOI : 10.4064/sm-120-3-247-258
Mots-clés : inductive and projective limits, acyclicity, derived projective limit functor

Jochen Wengenroth 1

1 
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Jochen Wengenroth. Acyclic inductive spectra of Fréchet spaces. Studia Mathematica, Tome 120 (1996) no. 3, pp. 247-258. doi: 10.4064/sm-120-3-247-258

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