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1997 | 122 | 2 | 139-151
Tytuł artykułu

Spaces of holomorphic mappings on Banach spaces with a Schauder basis

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We show that if U is a balanced open subset of a separable Banach space with the bounded approximation property, then the space ℋ(U) of all holomorphic functions on U, with the Nachbin compact-ported topology, is always bornological.
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autor
  • Instituto de Matemática, Universidade Estadual de Campinas, Caixa Postal 6065, 13081-970 Campinas, SP, Brazil, mujica@ime.unicamp.br
Bibliografia
  • [1] R. Aron, L. A. Moraes and R. Ryan, Factorization of holomorphic mappings in infinite dimensions, Math. Ann. 277 (1987), 617-628.
  • [2] S. B. Chae, Holomorphic germs on Banach spaces, Ann. Inst. Fourier (Grenoble) 21 (3) (1971), 107-141.
  • [3] G. Coeuré, Fonctions plurisousharmoniques sur les espaces vectoriels topologiques et applications à l'étude des fonctions analytiques, ibid. 20 (1) (1970), 361-432.
  • [4] G. Coeuré, Fonctionnelles analytiques sur certains espaces de Banach, ibid. 21 (2) (1971), 15-21.
  • [5] S. Dineen, The Cartan-Thullen theorem for Banach spaces, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 24 (1970), 667-676.
  • [6] S. Dineen, Holomorphy types on a Banach space, Studia Math. 39 (1971), 241-288.
  • [7] S. Dineen, Bounding subsets of a Banach space, Math. Ann. 192 (1971), 61-70.
  • [8] S. Dineen, Holomorphic functions on $(c_0, X_b)$-modules, ibid. 196 (1972), 106-116.
  • [9] S. Dineen, Complex Analysis in Locally Convex Spaces, North-Holland Math. Stud. 57, North-Holland, Amsterdam, 1981.
  • [10] L. Gruman et C. Kiselman, Le problème de Levi dans les espaces de Banach à base, C. R. Acad. Sci. Paris 274 (1972), 1296-1299.
  • [11] Y. Hervier, Sur le problème de Levi pour les espaces étalés banachiques, ibid. 275 (1972), 821-824.
  • [12] W. Johnson, H. Rosenthal and M. Zippin, On bases, finite-dimensional decompositions and weaker structures in Banach spaces, Israel J. Math. 9 (1971), 488-506.
  • [13] B. Josefson, A counterexample in the Levi problem, in: Proceedings on Infinite Dimensional Holomorphy, T. Hayden and T. Suffridge (eds.), Lecture Notes in Math. 364, Springer, Berlin, 1974, 168-177.
  • [14] Y. Katznelson, An Introduction to Harmonic Analysis, Wiley, New York, 1968.
  • [15] J. Mujica, Holomorphic approximation in Fréchet spaces with basis, J. London Math. Soc. 29 (1984), 113-126.
  • [16] J. Mujica, Holomorphic approximation in infinite-dimensional Riemann domains, Studia Math. 82 (1985), 107-134.
  • [17] J. Mujica, Complex Analysis in Banach Spaces, North-Holland Math. Stud. 120, North-Holland, Amsterdam, 1986.
  • [18] L. Nachbin, On the topology of the space of all holomorphic functions on a given open subset, Indag. Math. 29 (1967), 366-368.
  • [19] L. Nachbin, Concerning spaces of holomorphic mappings, lecture notes, Rutgers Univ., New Brunswick, N.J., 1970.
  • [20] L. Nachbin, Sur les espaces vectoriels topologiques d'applications continues, C. R. Acad. Sci. Paris 271 (1970), 596-598.
  • [21] P. Noverraz, Pseudo-convexité, convexité polynomiale et domaines d'holomorphie en dimension infinie, North-Holland Math. Stud. 3, North-Holland, Amsterdam, 1973.
  • [22] P. Noverraz, Approximation of holomorphic or plurisubharmonic functions in certain Banach spaces, in: Proceedings on Infinite Dimensional Holomorphy, T. Hayden and T. Suffridge (eds.), Lecture Notes in Math. 364, Springer, Berlin, 1974, 178-185.
  • [23] A. Pełczyński, On the impossibility of embedding of the space L in certain Banach spaces, Colloq. Math. 8 (1961), 199-203.
  • [24] A. Pełczyński, Any separable Banach space with the bounded approximation property is a complemented subspace of a Banach space with a basis, Studia Math. 40 (1971), 239-243.
  • [25] M. Schottenloher, The Levi problem for domains spread over locally convex spaces with a finite-dimensional Schauder decomposition, Ann. Inst. Fourier (Grenoble) 26 (4) (1976), 207-237.
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Bibliografia
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bwmeta1.element.bwnjournal-article-smv122i2p139bwm
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