Espacios de aplicaciones lineales
DOI:
https://doi.org/10.22199/S07160917.1985.0010.00004Keywords:
Aplicaciones línealesAbstract
Sean E, F espacios vectoriales topológicos sobre un cuerpo valuado (K, || ).
u : E ?. F una aplicación lineal.
u es continua ssi u es continua en el origen.
La suficiencia sigue de la linealidad de u y de la forma que tienen las vecindades de los puntos en un espacio vectorial topológico.
References
[1] S. BANACH. Theorie des operators lineaires. Warsav 1932.
[2] N. BOURBAKI. Espaces Vectoriels topologigues Ch. 3,4,5. Hermann 1967
[3] T. HUSAIN. The open mapping and closed graph Theorems in Topological vector spaces. Oxford Math. Monographs (1965).
[4] A. INGLETON. The Hahn - Banach Theorem for non-Archimedean valued fields. Proc. Camb. Phi1. Soc. 48 (1952), 41-45.
[5] S. IYAHEN. Barrelled spaces and the open mapping Theorem. J. London. M. Soc. (2) 11 (1975), 421-422.
[6] M. MAHOWALD. Barrelled spaces and the closed graph Theorem. J. London. M. Soc. 36 (1961), 108-110.
[7] A. MONNA. Functional Analysis in historical perspective. Utrecht. 1973.
[8] L. NACHBIN. A theorem of the Hahn - Banach type for linear transformation, Tran. A.M.S., 68 (1950), 28-46.
[9] S. OHWAKI. On Linear operators with closed range. Proc. Japan Acad. 50 (1974), 97-99.
[10] V. PTAK. A QUantitative refinament of the closed graph theorem. Czechoslovak Math J. 24 (99), 1974.
[11] H. SCHAEFER. Topological Vector Spaces. Springer Verlag. 1980.
[12] F. TREVES. Topological Vector Spaces, Distributions and Kernels. Academic Press. 1967.
[2] N. BOURBAKI. Espaces Vectoriels topologigues Ch. 3,4,5. Hermann 1967
[3] T. HUSAIN. The open mapping and closed graph Theorems in Topological vector spaces. Oxford Math. Monographs (1965).
[4] A. INGLETON. The Hahn - Banach Theorem for non-Archimedean valued fields. Proc. Camb. Phi1. Soc. 48 (1952), 41-45.
[5] S. IYAHEN. Barrelled spaces and the open mapping Theorem. J. London. M. Soc. (2) 11 (1975), 421-422.
[6] M. MAHOWALD. Barrelled spaces and the closed graph Theorem. J. London. M. Soc. 36 (1961), 108-110.
[7] A. MONNA. Functional Analysis in historical perspective. Utrecht. 1973.
[8] L. NACHBIN. A theorem of the Hahn - Banach type for linear transformation, Tran. A.M.S., 68 (1950), 28-46.
[9] S. OHWAKI. On Linear operators with closed range. Proc. Japan Acad. 50 (1974), 97-99.
[10] V. PTAK. A QUantitative refinament of the closed graph theorem. Czechoslovak Math J. 24 (99), 1974.
[11] H. SCHAEFER. Topological Vector Spaces. Springer Verlag. 1980.
[12] F. TREVES. Topological Vector Spaces, Distributions and Kernels. Academic Press. 1967.
Published
2018-03-28
How to Cite
[1]
S. Navarro Hernández, “Espacios de aplicaciones lineales”, Proyecciones (Antofagasta, On line), vol. 4, no. 10, pp. 35-56, Mar. 2018.
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