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2000 | 142 | 2 | 187-200

Tytuł artykułu

The space of real-analytic functions has no basis

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Języki publikacji

EN

Abstrakty

EN
Let Ω be an open connected subset of $ℝ^d$. We show that the space A(Ω) of real-analytic functions on Ω has no (Schauder) basis. One of the crucial steps is to show that all metrizable complemented subspaces of A(Ω) are finite-dimensional.

Czasopismo

Rocznik

Tom

142

Numer

2

Strony

187-200

Opis fizyczny

Daty

wydano
2000
otrzymano
2000-03-06

Twórcy

  • Faculty of Mathematics and Computer Science, A. Mickiewicz University, Matejki 48/49, 60-769 Poznań, Poland
autor
  • FB Mathematik, Bergische Universität Wuppertal, Gauß str. 20, D-42097 Wuppertal, Germany

Bibliografia

  • [1] S. Banach, eorja operacyj, tom I. Operacje liniowe [Theory of operators, vol. I. Linear operators], Kasa Mianowskiego, Warszawa, 1931 (in Polish).
  • [2] S. Banach, Théorie des opérations linéaires, Monografie Mat. 1, Warszawa, 1932.
  • [3] C. Bessaga, A nuclear Fréchet space without basis I. Variation on a theme of Djakov and Mitiagin, Bull. Acad. Polon. Sci. 24 (1976), 471-473.
  • [4] J. Bonet and P. Domański, Real analytic curves in Fréchet spaces and their duals, Monatsh. Math. 126 (1998), 13-36.
  • [5] J. Bonet and P. Domański, Parameter dependence of solutions of partial differential equations in spaces of real analytic functions, Proc. Amer. Math. Soc., to appear.
  • [6] P. B. Djakov and B. S. Mityagin, Modified construction of a nuclear Fréchet space without a basis, J. Funct. Anal. 23 (1976), 415-423.
  • [7] P. Domański and D. Vogt, A splitting theory for the space of distributions, Studia Math. 140 (2000), 57-77.
  • [8] E. Dubinsky, Nuclear Fréchet spaces without the bounded approximation property, ibid. 71 (1981), 85-105.
  • [9] P. Enflo, A counterexample to the approximation property in Banach spaces, Acta Math. 130 (1973), 309-317.
  • [10] A. Grothendieck, Produits tensoriels topologiques et espaces nucléaires, Mem. Amer. Math. Soc. 16 (1955).
  • [11] L. Hörmander, On the existence of real analytic solutions of partial differential equations with constant coefficients, Invent. Math. 21 (1973), 151-182.
  • [12] H. Jarchow, Locally Convex Spaces, B. G. Teubner, Stuttgart, 1981.
  • [13] M. Klimek, Pluripotential Theory, Clarendon Press, Oxford, 1991.
  • [14] S. Krantz, Function Theory of Several Complex Variables, Wiley, New York, 1982.
  • [15] S. Krantz and H. R. Parks, A Primer of Real Analytic Functions, Birkhäuser, Basel, 1992.
  • [16] A. Kriegl and P. W. Michor, The convenient setting for real analytic mappings, Acta Math. 165 (1990), 105-159.
  • [17] A. Kriegl and P. W. Michor, The Convenient Setting of Global Analysis, Amer. Math. Soc., Providence, 1997.
  • [18] M. Langenbruch, Continuous linear right inverses for convolution operators in spaces of real analytic functions, Studia Math. 110 (1994), 65-82.
  • [19] M. Langenbruch, Hyperfunction fundamental solutions of surjective convolution operators on real analytic functions, J. Funct. Anal. 131 (1995), 78-93.
  • [20] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces, Vol. I, Springer, Berlin, 1977.
  • [21] A. Martineau, Sur les fonctionnelles analytiques et la transformation de Fourier-Borel, J. Anal. Math. 11 (1963), 1-164.
  • [22] A. Martineau, Sur la topologie des espaces de fonctions holomorphes, Math. Ann. 163 (1966), 62-88.
  • [23] R. D. Mauldin (ed.), The Scottish Book, Birkhäuser, Boston, 1981.
  • [24] R. Meise and D. Vogt, Introduction to Functional Analysis, Clarendon Press, Oxford, 1997.
  • [25] B. S. Mityagin and G. M. Henkin, Linear problems of complex analysis, Uspekhi Mat. Nauk. 26 (1971), no. 4, 93-152 (in Russian); English transl.: Russian Math. Surveys 26 (1971), no. 4, 99-164.
  • [26] B. S. Mityagin et N. M. Zobin, Contre-exemple à l'existence d'une base dans un espace de Fréchet nucléaire, C. R. Acad. Sci. Paris Sér. A 279 (1974), 255-258, 325-327.
  • [27] V. B. Moscatelli, Fréchet space without continuous norms and without bases, Bull. London Math. Soc. 12 (1980), 63-66.
  • [28] V. P. Palamodov, Functor of projective limit in the category of topological vector spaces, Mat. Sb. 75 (1968), 567-603 (in Russian); English transl.: Math. USSR-Sb. 4 (1969), 529-559.
  • [29] V. P. Palamodov, Homological methods in the theory of locally convex spaces, Uspekhi Mat. Nauk 26 (1971), no. 1, 3-66 (in Russian); English transl.: Russian Math. Surveys 26 (1971), no. 1, 1-64.
  • [30] A. Pełczyński and C. Bessaga, Some aspects of the present theory of Banach spaces, in: S. Banach, Oeuvres, Vol. II, PWN, Warszawa, 1979, 222-302.
  • [31] A. Pietsch, Nuclear Locally Convex Spaces, Akademie-Verlag, Berlin, 1972.
  • [32] A. Szankowski, B(H) does not have the approximation property, Acta Math. 147 (1981), 89-108.
  • [33] D. Vogt, Charakterisierung der Unterräume eines nuklearen stabilen Potenzreihenraumes von endlichem Typ, Studia Math. 71 (1982), 251-270.
  • [34] D. Vogt, Frécheträume, zwischen denen jede stetige lineare Abbildung beschränkt ist, J. Reine Angew. Math. 345 (1983), 182-200.
  • [35] D. Vogt, An example of a nuclear Fréchet space without the bounded approximation property, Math. Z. 182 (1983), 265-267.
  • [36] D. Vogt, Lectures on projective spectra of DF-spaces, seminar lectures, AG Funktionalanalysis, Düsseldorf/Wuppertal, 1987.
  • [37] D. Vogt, Topics on projective spectra of LB-spaces, in: Advances in the Theory of Fréchet Spaces, T. Terzioğlu (ed.), Kluwer, Dordrecht, 1989, 11-27.
  • [38] J. Wengenroth, Acyclic inductive spectra of Fréchet spaces, Studia Math. 120 (1996), 247-258.
  • [39] P. Wojtaszczyk, The Franklin system is an unconditional basis in $H^1$, Ark. Mat. 20 (1982), 293-300.
  • [40] V. P. Zaharjuta, Spaces of analytic functions and complex potential theory, in: Linear Topological Spaces and Complex Analysis 1, A. Aytuna (ed.), METU- TÜBİTAK, Ankara, 1994, 74-146.
  • [41] V. P. Zaharjuta, Extremal plurisubharmonic functions, Hilbert scales, and the isomorphism of spaces of analytic functions of several variables, I, II, Teor. Funktsiĭ Funktsional. Anal. i Prilozhen. 19 (1974), 133-157; 21 (1974), 65-83 (in Russian).

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