Representation theorems of linear operators on p-adic function spaces

• Aguayo, José ^[1] ; Chandía, Elsa ^[1] ; Ojeda, Jacqueline ^[1]
  1. [1] Universidad de Concepción

     Universidad de Concepción

     Comuna de Concepción, Chile

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 23, Nº. 2, 2004, págs. 97-110
• Idioma: inglés
• DOI: 10.4067/S0716-09172004000200003
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• Resumen

  • Let X be a 0-dimensional Hausforff topological space, E, F nonarchimedean Banach spaces and Cb(X, E) the space of all continuous E-valued functions on X provided with two strict topologies. In this paper we show that every F-valued linear operator which is strictly continuous can be represented by a certain L(E, F )-valued measure defined on the ring of all clopen subsets of X.

• Referencias bibliográficas
  • Citas [1] J. Aguayo and J. Sanchez, Weakly compact operators and the strict topologies, Bulletin of the Australian Mathematical Society,...
  • [2] J. Aguayo, N. De Grande-De Kimpe, S. Navarro, Strict locally convex topologies on BC(X, K), Proc. p-Adic Functional Analysis, Marcel Dekker,...
  • [3] J. Aguayo, N. De Grande-De Kimpe, S. Navarro, Strict topologies and duals in spaces of functions, Proc. p-Adic Functional Analysis, Marcel...
  • [4] J. Diestel and J. Uhl, Vector Measures, Mathematical Surveys and Monographs, Number 15, A.M.S., (1977).
  • [5] A. Katsaras; Strict topologies in non-archimedean Function Spaces. Internat. J. Math. & Math. Sci., Vol 1, pp. 23-33, (1984).
  • [6] A. Katsaras, Integral Representation of Continuous Linear Operators on p-adic Function Spaces, Proc. p-Adic Functional Analysis, Marcel...
  • [7] A.C.M. Van Rooij; Non-archimedean functional analysis Marcel Dekker, (1978).
  • [8] R.F.Wheeler, A survey of Baire measure y strict topologies, Expo. Math., 2, pp. 97-190, (1983).