Representation theorems of linear operators on p-adic function spaces

  • José Aguayo Universidad de Concepción.
  • Elsa Chandía Universidad de Concepción.
  • Jacqueline Ojeda Universidad de Concepción.
Palabras clave: Banach spaces, F−valued linear operator, continuity, espacios de Banach, operador lineal F-valuado, continuidad.

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.

Biografía del autor

José Aguayo, Universidad de Concepción.
Facultad de Ciencias Físicas y Matemática,Departamento de Matemática.
Elsa Chandía, Universidad de Concepción.
Facultad de Ciencias Físicas y Matemática,Departamento de Matemática.
Jacqueline Ojeda, Universidad de Concepción.
Facultad de Ciencias Físicas y Matemática,Departamento de Matemática.

Citas

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[3] J. Aguayo, N. De Grande-De Kimpe, S. Navarro, Strict topologies and duals in spaces of functions, Proc. p-Adic Functional Analysis, Marcel Dekker, Inc., pp. 1 − 10, (1999).110 José Aguayo, Elsa Chandía and Jacqueline Ojeda

[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 Dekker, Inc., Vol 222, pp. 161-175, (2001).

[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).
Publicado
2017-05-22
Cómo citar
Aguayo, J., Chandía, E., & Ojeda, J. (2017). Representation theorems of linear operators on p-adic function spaces. Proyecciones. Journal of Mathematics, 23(2), 97-110. https://doi.org/10.4067/S0716-09172004000200003
Sección
Artículos