Artículo Original
Publicado 2018-07-22
Palabras clave
- espacios de Banach C(K),
- teorema de Banach-Stone
Cómo citar
Rincón-Villamizar, M. A. (2018). Una prueba del teorema de Holsztyński. Revista Integración, Temas De matemáticas, 36(1), 59–65. https://doi.org/10.18273/revint.v36n1-2018005
Resumen
Dado un espacio compacto Hausdorff, denotaremos por C(K) el espacio de Banach de las funciones continuas definidas en K con valores en R o C. Un resultado clásico en la teoría de Espacios de Banach de funciones continuas es el teorema de Holsztyński el cual establece que si C(K) es isométrico a un subespacio de C(S), entonces K es imagen continua de un subespacio de S. El objetivo de este artículo es dar una prueba alternativa de este resultado para subespacios extremadamente regulares de C(K).
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Referencias
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[2] Araujo J., Font J.J. and Hernández S., “A note on Holsztynski’s theorem”, Papers on general topology and applications, in Ann. New York Acad. Sci. 788, New York (1996), 9–12.
[3] Arens R.F. and Kelley J.L., “Characterization of the space of continuous functions over a compact Hausdorff space”, Trans. Amer. Math. Soc. 62 (1947), 499–508.
[4] Banach S., Théorie des opérations linéaires, Monografie Matematyczne, Warsaw, 1933.
[5] Behrends E., M-Sctructure and Banach-Stone theorem, Lecture Notes in Math. 736, Springer-Verlag, 1979.
[6] Cengiz B., “Continuous maps induced by isomorphisms of extremely regular function spaces”, J. Pure Appl. Sci. 18 (1985), No. 3, 377–384.
[7] Folland G.B., Real analysis, Modern techniques and their applications, Pure and Applied Mathematics (New York), A Wiley-Interscience Publication, John Wiley & Sons Inc., New York, 1999.
[8] Holsztyński W., “Continuous mappings induced by isometries of spaces of continuous functions”, Studia Math. 26 (1966), 133–136.
[9] Plebanek G., “On isomorphisms of Banach spaces of continuous functions”, Israel J. Math. 209 (2015), No. 1, 1–13.
[10] Semadeni Z., Banach spaces of Continuous Functions, Vol. 1, Monografie Mat. 55, PWN-Polish Sci. Publ. Warszawa, 1971.
[11] Stone M.H., “Applications of the theory of Boolean rings to general topology”, Trans. Amer. Math. Soc. 41 (1937), 375–481.