Publication: The compact open and the Nachbin ported topologies on spaces of holomorphic functions
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Publication Date
1988
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Birkhäuser Verlag
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Abstract
Some examples of Fréchet Montel spaces E, which are not Schwartz spaces, for which the compact open and the Nachbin ported topologies coincide on the space of all holomorphic functions on an arbitrary balanced open subset of E, are given.
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J. M. Ansemil and S. Ponte, Topologies associated with the compact open topology onH(U). Proc. Royal Irish Acad. Sect. A82, 121-128 (1982).
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).
S.Dineen, Complex analysis in locally convex spaces. North-Holland Mat. Studies57 (1981).
K. Floret, Fréchet-Montel spaces which are not Schwartz spaces. Portugal. Math.42, 1-4 (1983-84).
A. Grothendieck, Sur les espaces (F) and (DF). Summa Brasiliensis Math.3, 57-122 (1954).
A.Grothendieck, Produits tensoriels topologiques et espaces nucléaires. Mem. Amer. Math. Soc.16 (1955).
J.Horwath, Topological vector spaces and distributions. Reading, Massachusetts 1966.
G.Köthe, Topological vector spaces II. Berlin-Heidelberg-New York 1979.
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).
J. Mujica, A Banach-Dieudonné theorem for germs of holomorphic functions. J. Funct. Anal. (1)57, 31-48 (1984).
J. Mujica, Holomorphic approximation in infinite-dimensional Riemann domains. Studia Math.82, 107-134 (1985).
L.Nachbin, Topology on spaces of holomorphic mappings. Ergeb. Math. Grenzgeb.47, 1969.
L. Nachbin, On pure uniform holomorphy in spaces of holomorphic germs. Results in Mathematics,8, 117-122 (1985).
J. Bonet andA. Defant, Projective tensor products of distinguished Fréchet spaces. Proc. Royal Irish Acad. Sect. A85, 193-200 (1985).