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1991-1992 | 101 | 1 | 83-104
Tytuł artykułu

Isomorphy classes of spaces of holomorphic functions on open polydiscs in dual power series spaces

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Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let Λ_R(α) be a nuclear power series space of finite or infinite type with lim_{j→∞} (1/j) log α_j = 0. We consider open polydiscs D_a in Λ_R(α)'_b with finite radii and the spaces H(D_a) of all holomorphic functions on D_a under the compact-open topology. We characterize all isomorphy classes of the spaces {H(D_a) | a ∈ Λ_R(α), a > 0}. In the case of a nuclear power series space Λ₁(α) of finite type we give this characterization in terms of the invariants (Ω̅ ) and (Ω̃ ) known from the theory of linear operators between Fréchet spaces.
Słowa kluczowe
Czasopismo
Rocznik
Tom
101
Numer
1
Strony
83-104
Opis fizyczny
Daty
wydano
1991
otrzymano
1990-01-17
Twórcy
  • Mathematisches Institut, Universität Düsseldorf, Có Prof. R. Meise, Universitätsstraße 1, D-4000 Düsseldorf, Germany
Bibliografia
  • [1] P. J. Boland and S. Dineen, Holomorphic functions on fully nuclear spaces, Bull. Soc. Math. France 106 (1978), 311-336.
  • [2] P. A. Chalov and V. P. Zakharyuta, A quasiequivalence criterion for absolute bases in an arbitrary (F)-space, Izv. Severo-Kavkaz. Nauchn. Tsentra Vyssh. Shkoly Estestv. Nauki 1983 (2), 22-24 (in Russian).
  • [3] P. B. Djakov, A short proof of the theorem of Crone and Robinson on quasi-equivalence of regular bases, Studia Math. 53 (1975), 269-271.
  • [4] H. Jarchow, Locally Convex Spaces, Teubner, 1981.
  • [5] R. Meise and D. Vogt, Structure of spaces of holomorphic functions on infinite dimensional polydiscs, Studia Math. 75 (1983), 235-252.
  • [6] R. Meise and D. Vogt, Analytic isomorphisms of infinite dimensional polydiscs and an application, Bull. Soc. Math. France 111 (1983), 3-20.
  • [7] R. Meise and D. Vogt, Holomorphic functions of uniformly bounded type on nuclear Fréchet spaces, Studia Math. 83 (1986), 147-166.
  • [8] R. Meise and D. Vogt, Holomorphic Functions on Nuclear Sequence Spaces, Departamento de Teoría de Funciones, Universidad Complutense, Madrid 1986.
  • [9] L. Mirsky, Transversal Theory, Academic Press, 1971.
  • [10] B. S. Mityagin, The equivalence of bases in Hilbert scales, Studia Math. 37 (1971), 111-137 (in Russian).
  • [11] A. Pietsch, Nuclear Locally Convex Spaces, Ergeb. Math. Grenzgeb. 66, Springer, 1972.
  • [12] H. H. Schaefer, Topological Vector Spaces, Springer, 1971.
  • [13] M. Scheve, Räume holomorpher Funktionen auf unendlich-dimensionalen Polyzylindern, Dissertation, Düsseldorf 1988.
  • [14] D. Vogt, Frécheträume, zwischen denen jede stetige lineare Abbildung beschränkt ist, J. Reine Angew. Math. 345 (1983), 182-200.
  • [15] M. J. Wagner, Unterräume und Quotienten von Potenzreihenräumen, Dissertation, Wuppertal 1977.
  • [16] V. P. Zakharyuta, Isomorphism and quasiequivalence of bases for Köthe power series spaces, in: Mathematical Programming and Related Problems (Proc. 7th Winter School, Drogobych 1974), Theory of Operators in Linear Spaces, Akad. Nauk SSSR, Tsentr. Ekon.-Mat. Inst., Moscow 1976, 101-126 (in Russian); see also Dokl. Akad. Nauk SSSR 221 (1975), 772-774 (in Russian).
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-smv101i1p83bwm
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