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1993 | 107 | 3 | 305-315
Tytuł artykułu

Montel and reflexive preduals of spaces of holomorphic functions on Fréchet spaces

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
For U open in a locally convex space E it is shown in [31] that there is a complete locally convex space G(U) such that $G(U)'_i = (ℋ (U),τ_δ)$. Here, we assume U is balanced open in a Fréchet space and give necessary and sufficient conditions for G(U) to be Montel and reflexive. These results give an insight into the relationship between the $τ_0$ and $τ_ω$ topologies on ℋ (U).
Słowa kluczowe
Czasopismo
Rocznik
Tom
107
Numer
3
Strony
305-315
Opis fizyczny
Daty
wydano
1993
otrzymano
1992-12-21
poprawiono
1993-04-27
Twórcy
Bibliografia
  • [1] R. Alencar, R. Aron and S. Dineen, A reflexive space of holomorphic functions in infinitely many variables, Proc. Amer. Math. Soc. 90 (1984), 407-411.
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  • [9] J. A. Barroso and L. Nachbin, Some topological properties of spaces of holomorphic mappings in infinitely many variables, in: Advances in Holomorphy, J. A. Barroso (ed.), North-Holland Math. Stud. 34, North-Holland, 1979, 67-91.
  • [10] K.-D. Bierstedt and J. Bonet, Density conditions in Fréchet and (DF)-spaces, Rev. Mat. Univ. Complut. Madrid 2 (1989), no. suplementario, 59-75.
  • [11] K.-D. Bierstedt and R. Meise, Aspects of inductive limits in spaces of germs of holomorphic functions on locally convex spaces and applications to a study of $(ℋ (U),τ_ω)$, in: Advances in Holomorphy, J. A. Barroso (ed.), North-Holland Math. Stud. 34, North-Holland, 1979, 111-178.
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  • [13] J. Bonet, J. C. Dí az and J. Taskinen, Tensor stable Fréchet and (DF) spaces, Collect. Math., to appear.
  • [14] C. Boyd, Distinguished preduals of the space of holomorphic functions, Rev. Mat. Univ. Complut. Madrid, to appear.
  • [15] P. G. Casazza and E. W. Odell, Tsirelson space, II, preprint.
  • [16] A. Defant and M. Maestre, Holomorphic functions and (BB)-property on Fréchet -Montel spaces, Math. Proc. Cambridge Philos. Soc., to appear.
  • [17] J. C. Dí az and A. M. Miñarro, Distinguished Fréchet spaces and projective tensor products, Doǧa Mat. 14 (1990), 191-208.
  • [18] J. C. Dí az and A. M. Miñarro, On Fréchet Montel spaces and projective tensor products, Math. Proc. Cambridge Philos. Soc., to appear.
  • [19] S. Dineen, Complex Analysis on Locally Convex Spaces, North-Holland Math. Stud. 57, North-Holland, 1981.
  • [20] S. Dineen, Holomorphic functions on Fréchet-Montel spaces, J. Math. Anal. Appl. 163 (1992), 581-587.
  • [21] S. Dineen, Quasinormable spaces of holomorphic functions, Note Mat., to appear.
  • [22] P. Galindo, D. García and M. Maestre, The coincidence of $τ_0$ and $τ_ω$ for spaces of holomorphic functions on some Fréchet-Montel spaces, Proc. Roy. Irish Acad. 91A (1991), 137-143.
  • [23] A. Grothendieck, Produits tensoriels topologiques et espaces nucléaires, Mem. Amer. Math. Soc. 16 (1955).
  • [24] J. Horváth, Topological Vector Spaces and Distributions, Vol. 1, Addison-Wesley, Reading, Mass., 1966.
  • [25] H. Jarchow, Locally Convex Spaces, B. G. Teubner, Stuttgart, 1981.
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  • [27] P. Mazet, Analytic Sets in Locally Convex Spaces, North-Holland Math. Stud. 89, North-Holland, 1984.
  • [28] R. Meise, A remark on the ported and the compact-open topology for spaces of holomorphic functions on nuclear Fréchet spaces, Proc. Roy. Irish Acad. 81A (1981), 217-223.
  • [29] J. Mujica, A Banach-Dieudonné theorem for the space of germs of holomorphic functions, J. Funct. Anal. 57 (1984), 31-48.
  • [30] J. Mujica, Holomorphic approximation in infinite-dimensional Riemann domains, Studia Math. 82 (1985), 107-134.
  • [31] J. Mujica and L. Nachbin, Linearization of holomorphic mappings on locally convex spaces, J. Math. Pures Appl. 71 (1992), 543-560.
  • [32] A. Peris, Productos tensoriales de espacios localmente convexos casinormables y otras clases relacionadas, thesis, Universidad de Valencia, 1992.
  • [33] R. Ryan, Applications of topological tensor products to infinite dimensional holomorphy, thesis, Trinity College Dublin, 1980.
  • [34] H. H. Schaefer, Topological Vector Spaces, 3rd printing corrected, Springer, 1971.
  • [35] J. Schmets, Espaces de fonctions continues, Lecture Notes in Math. 519, Springer, 1976.
  • [36] M. Schottenloher, $τ_ω=τ_0$ for domains in $ℂ^ℕ$, in: Infinite Dimensional Holomorphy and Applications, M. Matos (ed.), North-Holland Math. Stud. 12, North-Holland, 1977, 393-395.
  • [37] J. Taskinen, Examples of non-distinguished Fréchet spaces, Ann. Acad. Sci. Fenn. Ser. AI Math. 14 (1989), 75-88.
  • [38] B. S. Tsirelson, Not every Banach space contains an imbedding of $ℓ_p$ or $c_0$, Functional Anal. Appl. 8 (1974), 138-141.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-smv107i3p305bwm
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