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On two classes of (F)-spaces

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References

  1. K. D.Bierstedt, R.Meise and W. H.Summers, Köthe sets and Köthe sequence spaces. In: Functional Analysis, Holomorphy and Approximation Theory; J. A. Barroso (ed.), North-Holland Math. Studies71, 27–90 (1982).

  2. A. Grothendieck, Sur les espaces (F) et (DF). Summa Brasil. Math.3, 57–112 (1954).

    Google Scholar 

  3. A.Grothendieck, Produits tensoriels topologiques et espaces nucléaires. Mem. Amer. Math. Soc.16 (1955).

  4. H. Komatsu, Ultradistributions I, Structure theorems and a characterization. J. Fac. Sc. Univ. Tokyo, Sec. IA20, 25–105 (1973).

    Google Scholar 

  5. S. G. Krein, On an interpolation theorem in operator theory (Russian). Dokl. Akad. Nauk SSSR130, 491–494 (1960), English transl.: Soviet Math. Dokl.1, 61–64 (1960).

    Google Scholar 

  6. S. G. Krein, On the concept of a normal scale of spaces (Russian). Dokl Akad. Nauk SSSR132, 510–513 (1960), English transl.: Soviet Math. Dokl.1, 586–589 (1960).

    Google Scholar 

  7. S. G. Krein andY. I. Petunin, Scales of Banach spaces (Russian). Usp. Math. Nauk (2)21, 89–168 (1966), English transl: Russian Math. Surveys, (2)21, 85–159 (1966).

    Google Scholar 

  8. R.Meise and D.Vogt, A characterization of quasi-normable Fréchet spaces. To appear in Math. Nachr.

  9. B. S. Mityagin, Non Schwartzian power series spaces. Math. Z.182, 303–310 (1983).

    Google Scholar 

  10. V. P. Palamodov, Homological methods in the theory of locally convex spaces (Russian). Usp. Math. Nauk (1)26, 3–66 (1971), English transl.: Russian Math. Surveys (1)26, 1–64 (1971).

    Google Scholar 

  11. H. J. Petzsche, Die Nuklearität der Ultradistributionsräume und der Satz vom Kern I, II. Manuscripta math.24, 133–171 (1978),27, 221–251 (1979).

    Google Scholar 

  12. A.Pietsch, Nuclear locally convex spaces. Ergeb. Math. Grenzgeb.66, Berlin 1972.

  13. M. Valdivia, On quasi-normable echolon spaces. Proc. Edinburgh Math. Soc.24, 73–80 (1981).

    Google Scholar 

  14. M.Valdivia, Topics in locally convex spaces. Amsterdam 1982.

  15. D. Vogt, Charakterisierung der Unterräume vons. Math. Z.155, 109–117 (1977).

    Google Scholar 

  16. D.Vogt, Subspaces and quotients of (s). In: Functional Analysis, Surveys and Recent Results; K. D. Bierstedt, B. Fuchssteiner (eds.), North-Holland Math. Studies27, 167–187 (1977).

  17. D. Vogt, Ein Isomorphiesatz für Potenzreihenräume. Arch. Math.38, 540–548 (1982).

    Google Scholar 

  18. D.Vogt, Sequence space representations of spaces of test functions and distributions. In: Functional analysis, holomorphy, and approximation theory; G. Zapata (ed.), Lecture Notes in Pure and Appl. Math.83, 405–443, New York 1983.

  19. D. Vogt, Frécheträume, zwischen denen jede stetige lineare Abbildung beschränkt ist. J. Reine Angew. Math.345, 182–200 (1983).

    Google Scholar 

  20. D.Vogt, On the functors Ext1 (E, F) for Fréchet spaces. Preprint.

  21. D. Vogt undM. J. Wagner, Charakterisierung der Quotientenräume vons und eine Vermutung von Martineau. Studia Math.67, 225–240 (1980).

    Google Scholar 

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Vogt, D. On two classes of (F)-spaces. Arch. Math 45, 255–266 (1985). https://doi.org/10.1007/BF01275578

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