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A new characterization of $\operatorname{Proj}^1{\mathcal X}=0$
for countable spectra of (LB)-spaces


Author: Jochen Wengenroth
Journal: Proc. Amer. Math. Soc. 127 (1999), 737-744
MSC (1991): Primary 46A13, 46M15
DOI: https://doi.org/10.1090/S0002-9939-99-04559-1
MathSciNet review: 1468208
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Abstract | References | Similar Articles | Additional Information

Abstract: The derived projective limit functor Proj¹ is a very useful tool for investigating surjectivity problems in various parts of analysis (e.g. solvability of partial differential equations).

We provide a new characterization for vanishing Proj¹ on projective spectra of (LB)-spaces which improves a classical result of V. P. Palamodov and V. S. Retakh.


References [Enhancements On Off] (What's this?)

  • 1. J. Bonet, P. Doma\'{n}ski, Real analytic curves in Fréchet spaces and their duals, Monatsh. Math., to appear.
  • 2. N. Bourbaki, Eléments de mathématique, Topologie Générale I, Hermann, Paris (1974). MR 50:11111
  • 3. R. W. Braun, R. Meise, D. Vogt, Applications of the projective limit functor to convolutions and partial differential equations, pp. 29-46 in Advances in the Theory of Fréchet spaces, T. Terzio[??]glu (ed.), NATO ASF Ser. C 287, Kluwer, Dordrecht (1989). MR 92b:46119
  • 4. R. W. Braun, R. Meise, D. Vogt, Existence of fundamental solutions and surjectivity of convolution operators on classes of ultradifferentiable functions, Proc. London Math. Soc. 61 (1990), 344-370. MR 91i:46038
  • 5. R. W. Braun, D. Vogt, A sufficient condition for $\operatorname{Proj}^1 = 0$, Michigan Math. J. 44 (1997), 149-156. MR 98c:46162
  • 6. L. Frerick, J. Wengenroth, A sufficient condition for vanishing of the derived projective limit functor, Archiv Math. (Basel) 67 (1996), 296-301. MR 97g:46095
  • 7. V. P. Palamodov, The projective limit functor in the category of linear topological spaces, Mat. Sbornik 75 (1968), 567-603 (in Russian); English transl.: Math. USSR - Sb 4 (1968), 529-558. MR 36:6898
  • 8. V. P. Palamodov, Homological methods in the theory of locally convex spaces, Uspekhi Mat. Nauk 26 (1971), 3 - 65 (in Russian); English transl.: Russian Math. Surveys 26 (1971), 1-64. MR 45:2442
  • 9. V. S. Retakh, Subspaces of a countable inductive limit, Dokl. Akad. Nauk SSSR 194 (1970), 1277-1279 (in Russian); English transl.: Soviet Math. Dokl. 11 (1970), 1384-1386. MR 44:2018
  • 10. D. Vogt, On the functors Ext$^{1}(E,F)$ for Fréchet spaces, Studia Math. 85 (1987), 163-197. MR 89a:46146
  • 11. D. Vogt, Lectures on projective spectra of (DF)-spaces, Seminar lectures, AG Funktionalanalysis Düsseldorf/Wuppertal (1987).
  • 12. D. Vogt, Topics on projective spectra of (LB)-spaces, pp. 11-27 in Advances in the Theory of Fréchet spaces, T. Terzio[??]glu (ed.), NATO ASF Ser. C 287, Kluwer, Dordrecht (1989). MR 93b:46011
  • 13. D. Vogt, Regularity properties of (LF)-spaces, pp. 57-84 in Progress in Functional Analysis, North-Holland Math. Studies 170 (1992). MR 93b:46012
  • 14. J. Wengenroth, Acyclic inductive spectra of Fréchet spaces, Studia Math. 120 (3) (1996), 247-258. MR 97m:46006

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Additional Information

Jochen Wengenroth
Affiliation: FB IV – Mathematik, Universität Trier, D – 54286 Trier, Germany
Email: wengen@uni-trier.de

DOI: https://doi.org/10.1090/S0002-9939-99-04559-1
Keywords: Derived projective limit functor, Retakh's condition, weakly acyclic (LF)-spaces
Received by editor(s): January 9, 1997
Received by editor(s) in revised form: June 10, 1997
Additional Notes: The main result of this paper was obtained during a visit at the Polytechnical University of Valencia in March 1996. The author thanks J. Bonet and A. Peris for their kind hospitality.
Communicated by: Dale Alspach
Article copyright: © Copyright 1999 American Mathematical Society

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