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1995 | 113 | 1 | 43-54
Tytuł artykułu

Holomorphic functions and Banach-nuclear decompositions of Fréchet spaces

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Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We introduce a decomposition of holomorphic functions on Fréchet spaces which reduces to the Taylor series expansion in the case of Banach spaces and to the monomial expansion in the case of Fréchet nuclear spaces with basis. We apply this decomposition to obtain examples of Fréchet spaces E for which the τ_{ω} and τ_{δ} topologies on H(E) coincide. Our result includes, with simplified proofs, the main known results-Banach spaces with an unconditional basis and Fréchet nuclear spaces with DN [2, 4, 5, 6] - together with new examples, e.g. Banach spaces with an unconditional finite-dimensional Schauder decomposition and certain Fréchet-Schwartz spaces. This gives the first examples of Fréchet spaces, which are not nuclear, with τ_{0} = τ_{δ} on H(E).
Słowa kluczowe
Czasopismo
Rocznik
Tom
113
Numer
1
Strony
43-54
Opis fizyczny
Daty
wydano
1995
otrzymano
1993-05-19
poprawiono
1994-06-27
Twórcy
autor
  • Department of Mathematics, University College Dublin, Belfield, Dublin 4, Ireland
Bibliografia
  • [1] J. Bonet and J. C. Díaz, The problem of topologies of Grothendieck and the class of Fréchet T-spaces, Math. Nachr. 150 (1991), 109-118.
  • [2] G. Coeuré, Fonctions analytiques sur certains espaces de Banach, Ann. Inst. Fourier (Grenoble) 21 (2) (1971), 15-21.
  • [3] S. Dineen, Bounding subsets of a Banach space, Math. Ann. 192 (1971), 61-70.
  • [4] S. Dineen, Holomorphic functions on $(c_0,X_b)$-modules, ibid. 196 (1972), 106-116.
  • [5] S. Dineen, Complex Analysis in Locally Convex Spaces, North-Holland Math. Stud. 57, North-Holland, 1981.
  • [6] S. Dineen, Analytic functionals on fully nuclear spaces, Studia Math. 73 (1982), 11-32.
  • [7] S. Dineen, Holomorphic functions and the (BB)-property, Math. Scand., to appear.
  • [8] N. J. Kalton and N. T. Peck, Twisted sums of sequence spaces and the three space problem, Trans. Amer. Math. Soc. 255 (1979), 1-30.
  • [9] T. Ketonen, On unconditionality in $L_p$-spaces, Ann. Acad. Sci. Fenn. Dissertationes 35 (1981).
  • [10] G. Metafune, Quojections and finite dimensional decompositions, preprint.
  • [11] D. Vogt, Subspaces and quotients of (s), in: Functional Analysis: Surveys and Recent Results, K. D. Bierstedt and B. Fuchsteiner (eds.), North-Holland Math. Stud. 27, North-Holland, 1977, 167-187.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-smv113i1p43bwm
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