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The compact open and the Nachbin ported topologies on spaces of holomorphic functions

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References

  1. J. M. Ansemil andS. Ponte, Topologies associated with the compact open topology onH(U). Proc. Royal Irish Acad. Sect. A82, 121–128 (1982).

    Google Scholar 

  2. K. D.Biersted, R. G.Meise and W. H.Summers, Köthe sets and Köthe sequence spaces. Proc. of the Seminar on Functional Analysis, Holomorphy and Approximation Theory. J. A. Barroso Editor; North-Holland Mat. Studies71, 27–91 (1982).

  3. S.Dineen, Complex analysis in locally convex spaces. North-Holland Mat. Studies57 (1981).

  4. K. Floret, Fréchet-Montel spaces which are not Schwartz spaces. Portugal. Math.42, 1–4 (1983–84).

    Google Scholar 

  5. A. Grothendieck, Sur les espaces (F) and (DF). Summa Brasiliensis Math.3, 57–122 (1954).

    Google Scholar 

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

  7. J.Horwath, Topological vector spaces and distributions. Reading, Massachusetts 1966.

  8. G.Köthe, Topological vector spaces II. Berlin-Heidelberg-New York 1979.

  9. R. G. Meise, A remark on the ported and compact open topology for spaces of holornorphic functions on nuclear Fréchet spaces. Proc. Royal Irish Acad. Sect. A (2)81, 217–233 (1981).

    Google Scholar 

  10. J. Mujica, A Banach-Dieudonné theorem for germs of holomorphic functions. J. Funct. Anal. (1)57, 31–48 (1984).

    Google Scholar 

  11. J. Mujica, Holomorphic approximation in infinite-dimensional Riemann domains. Studia Math.82, 107–134 (1985).

    Google Scholar 

  12. L.Nachbin, Topology on spaces of holomorphic mappings. Ergeb. Math. Grenzgeb.47, 1969.

  13. L. Nachbin, On pure uniform holomorphy in spaces of holomorphic germs. Results in Mathematics,8, 117–122 (1985).

    Google Scholar 

  14. J. Bonet andA. Defant, Projective tensor products of distinguished Fréchet spaces. Proc. Royal Irish Acad. Sect. A85, 193–200 (1985).

    Google Scholar 

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Author notes

  1. J. M. Ansemil & S. Ponte

    Present address: Departamento de Análisis Matemático Facultad de Matemáticas, Universidad Complutense, Ciudad Universitaria, 28040, Madrid, Spain

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    1. J. M. Ansemil
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    2. S. Ponte
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    Additional information

    Supported by the C.A.I.C.Y.T. of Spain. Project 2197/83.

    The authors thank Profs. S. Dineen and R. Meise for some helpful discussions.

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    Ansemil, J.M., Ponte, S. The compact open and the Nachbin ported topologies on spaces of holomorphic functions. Arch. Math 51, 65–70 (1988). https://doi.org/10.1007/BF01194156

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