Pacific Journal of Mathematics

Grothendieck locally convex spaces of continuous vector valued functions.

Francisco J. Freniche

Article information

Pacific J. Math., Volume 120, Number 2 (1985), 345-355.

First available in Project Euclid: 8 December 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 46E40: Spaces of vector- and operator-valued functions
Secondary: 46E10: Topological linear spaces of continuous, differentiable or analytic functions


Freniche, Francisco J. Grothendieck locally convex spaces of continuous vector valued functions. Pacific J. Math. 120 (1985), no. 2, 345--355.

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  • [1] G. Y. H. Chi, On the Radon-Nikodym theorem and locally convex spaces with the Radon-Nikodym property, Proc. Amer. Math. Soc, 61 (1977), 245-253.
  • [2] F. J. Freriiche, Barrelledness of the space of vector valued and simple functions, Math. Ann., 267 (1984), 479-486.
  • [3] F. J. Freriiche, The Vitali-Hahn-Saks theorem for Boolean algebras with the subsequential interpolation property, Proc. Amer. Math. Soc,92 (1984),362-366.
  • [4] R. Haydon, Trois exemples dans la theorie des espaces de fonctions continues, C. R. Acad. Sci. Paris, 276A, (1973),685-687.
  • [5] R. Hollstein, Permanence properties of <g(X, E), Manuscripta Math., 38 (1982), 41-58.
  • [6] R. Isbell and Z. Semadeni, Projections constants and spaces of continuous functions, Trans. Amer. Math. Soc, 107 (1963), 38-48.
  • [7] H. Jarchow, Locally Convex Spaces, Stuttgart, B. G. Teubner 1981.
  • [8] J. Mendoza, Barrelledness conditions on ?(, E) and &(9 E), Math. Ann., 261 (1982), 11-22.
  • [9] J. Mendoza, Necessary and sufficient conditions for C(X, E) to be barrelled or infrabar- relled, Simon Stevin,57 (1983), 103-123.
  • [10] J. Mjica, Spaces of continuous functions with values in an inductive limit, Lecture Notes in Pures and Applied Math., 83(1983).
  • [11] A. Nissenzweig,w*-sequentialconvergence, Israel J. Math., 22 (1975),266-272.
  • [12] A. Pietsch, Nuclear Locally Convex Spaces, Berlin-Heidelberg-New York, Springer 1972.
  • [13] W. Schachermayer, On some classical measure-theoretic theorems for non-sigma-com- plete Boolean algebras, Johannes Kepler Universit'at Linz, Linz-Auhof1980.
  • [14] J. Schmets, Spaces of Vector-Valued Continuous Functions, Lecture Notes in Math. 1003, Berlin-Heidelberg-New York-Tokyo,Springer1983.
  • [15] A. H. Suchat, Integral representations theorems in topological vector spaces, Trans. Amer. Math. Soc, 172 (1972), 373-397.
  • [16] S. Warner, The topology of compact convergence on continuousfunctions spaces, Duke Math. J., 25 (1958), 265-282.
  • [17] A. Wilansky, Modern Methods in Topological Vector Spaces, NewYork, McGraw-Hill 1978.