Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

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

by Jochen Wengenroth
Proc. Amer. Math. Soc. 127 (1999), 737-744
DOI: https://doi.org/10.1090/S0002-9939-99-04559-1

Abstract:

The derived projective limit functor Proj$^1$ 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 Proj$^1$ on projective spectra of (LB)-spaces which improves a classical result of V. P. Palamodov and V. S. Retakh.
References
  • J. Bonet, P. Domański, Real analytic curves in Fréchet spaces and their duals, Monatsh. Math., to appear.
  • N. Bourbaki, Éléments de mathématique. Topologie générale. Chapitres 1 à 4, Hermann, Paris, 1971. MR 0358652
  • Rüdiger W. Braun, Reinhold Meise, and Dietmar Vogt, Applications of the projective limit functor to convolution and partial differential equations, Advances in the theory of Fréchet spaces (Istanbul, 1988) NATO Adv. Sci. Inst. Ser. C: Math. Phys. Sci., vol. 287, Kluwer Acad. Publ., Dordrecht, 1989, pp. 29–46. MR 1083556
  • R. W. Braun, R. Meise, and D. Vogt, Existence of fundamental solutions and surjectivity of convolution operators on classes of ultra-differentiable functions, Proc. London Math. Soc. (3) 61 (1990), no. 2, 344–370. MR 1063049, DOI 10.1112/plms/s3-61.2.344
  • Rüdiger W. Braun and Dietmar Vogt, A sufficient condition for $\textrm {Proj}^1{\scr X}=0$, Michigan Math. J. 44 (1997), no. 1, 149–156. MR 1439674, DOI 10.1307/mmj/1029005626
  • L. Frerick and J. Wengenroth, A sufficient condition for vanishing of the derived projective limit functor, Arch. Math. (Basel) 67 (1996), no. 4, 296–301. MR 1407332, DOI 10.1007/BF01197593
  • V. P. Palamodov, The projective limit functor in the category of topological linear spaces, Mat. Sb. (N.S.) 75 (117) (1968), 567–603 (Russian). MR 0223851
  • V. P. Palamodov, Homological methods in the theory of locally convex spaces, Uspehi Mat. Nauk 26 (1971), no. 1(157), 3–65 (Russian). MR 0293365
  • V. S. Retah, The subspaces of a countable inductive limit, Dokl. Akad. Nauk SSSR 194 (1970), 1277–1279 (Russian). MR 0284794
  • Dietmar Vogt, On the functors $\textrm {Ext}^1(E,F)$ for Fréchet spaces, Studia Math. 85 (1987), no. 2, 163–197. MR 887320, DOI 10.4064/sm-85-2-163-197
  • D. Vogt, Lectures on projective spectra of (DF)-spaces, Seminar lectures, AG Funktionalanalysis Düsseldorf/Wuppertal (1987).
  • Dietmar Vogt, Topics on projective spectra of (LB)-spaces, Advances in the theory of Fréchet spaces (Istanbul, 1988) NATO Adv. Sci. Inst. Ser. C: Math. Phys. Sci., vol. 287, Kluwer Acad. Publ., Dordrecht, 1989, pp. 11–27. MR 1083555
  • Dietmar Vogt, Regularity properties of (LF)-spaces, Progress in functional analysis (Peñíscola, 1990) North-Holland Math. Stud., vol. 170, North-Holland, Amsterdam, 1992, pp. 57–84. MR 1150738, DOI 10.1016/S0304-0208(08)70311-6
  • Jochen Wengenroth, Acyclic inductive spectra of Fréchet spaces, Studia Math. 120 (1996), no. 3, 247–258. MR 1410451, DOI 10.4064/sm-120-3-247-258
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 46A13, 46M15
  • Retrieve articles in all journals with MSC (1991): 46A13, 46M15
Bibliographic Information
  • Jochen Wengenroth
  • Affiliation: FB IV – Mathematik, Universität Trier, D – 54286 Trier, Germany
  • Email: wengen@uni-trier.de
  • 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
  • © Copyright 1999 American Mathematical Society
  • 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