A Nonstandard Proof of the Banach-Steinhaus Theorem

pp. 185-188The Banach-Steinhaus theorem, also known as Uniform Boundedness Principle, has a standard proof a little bit too long. In this article we will give a real short proof using the nonstandard analysis technique

Linear operations on locally convex topological vector spaces.

Our purpose is to extend, to the class of linear operators on a locally convex space, some of the results of spectral theory. In order to do this we had to introduce some topologies on the space of operators that are not locally convex. These topologies are of interest in their own right, and have proved useful in enabling us to attain our goal. There is an important class of topological vector spaces named ab-spaces (almost bornological spaces), but there are not too many facts about them. We briefly discuss some new results and give a characterization of those spaces in Chapter 3

p-Compact, p-Bounded and p-Complete

[EN] In this paper the nonstandard theory of uniform topological spaces isapplied with two main objectives: (1) to give a nonstandard treatmentof Bernstein’s concept of p-compactness with additional results, (2) tointroduce three new concepts (p,q)-compactness, p-totally boundednessand p-completeness. I prove some facts about them and how these threeconcepts are related with p-compactness.Vera Mendoza, R. (2011). p-Compact, p-Bounded and p-Complete. Applied General Topology. 12(1):17-25. doi:10.4995/agt.2011.1697.SWORD172512

A formula to calculate the spectral radius of a compact linear operator

There is a formula (Gelfand's formula) to find the spectral radius of a linear operator defined on a Banach space. That formula does not apply even in normed spaces which are not complete. In this paper we show a formula to find the spectral radius of any linear and compact operator T defined on a complete topological vector space, locally convex. We also show an easy way to find a non-trivial T-invariant closed subspace in terms of Minkowski functional

A characterization of Pontryagin–van Kampen

duality for locally convex spaces

Estado, nación y provincias en la Nueva Granada, siglo XIX

IP 1102-10-438-96Contrato; no. 561/96LIBRO : Figuraciones en proceso / compilado por Vera Weiler TESIS : Teatrodel 20 de julio : historia de la representacion patriotica del 20 de julio en Colombia (1814346610) / Beatriz Rincon de Reatiga -- La funcion politica de los textos de historia patria en el primer siglo dela republica colombiana / Martha Yaneth Silva Mendoza -- El estado y la decadencia de la esclavitud en Colombia 1821-1853 / Liliana Fabiola Ruiz Hernandez -- La prensa y la invencion del estado nacional (1810-1816) /Moises Araque Ortiz -- La gobernacion de Velez : funcionamiento politico administrativo y vinculacion al estadoneogranadino (1832-1858) / Nestor Moyano RodriguezSubproyecto 1. La provincia de Santa Marta, 1830 - 1845 /Rigoberto RuedaSantos -- Subproyecto 2. El canton;fortoul en la provincia Garcia Rovira 1851 - 1853 / NestorAndres GongoraRojas -- Subproyecto 3. Reformas;del ejercito neogranadino 1830- 1854 / Juan Alberto RuedaCardozo -- Subproyecto 4. Las provincias de;Mariquita y Neiva 1830 - 1854 / William Buendia Acevedo -'- Subproyecto 5.Riqueza y poder : la familia Plata;en Colombia (1780 - 1810) / Jacqueline Blanco Blanco -- Subproyecto 6. Elproyecto de incorporacion de los;indios a la nacion en la Nueva Granada (1740 - 1850) / Jairo Gutierrez Ramos -- Subproyecto 7. La provincia de;Tunja en el proceso de incorporacion al Estado Nacional 18-321845 / Maria Victoria Dotor Robayo --;Subproyecto 8. Estado, nacion y provincia de Antioquia : guerrras civilese invencin de la region 1829 - 1863;/ Fernando Botero Herrera -- Subproyecto 9. El Choco : configuracion regional en la primera mitad del Siglo;XIX/ Orian Jimenez Meneses. ARTICULO (S) EN REVISTA: MartinezGarnica, Armando. el movimiento historico de las;provincias neogranadinas. EN : Anuario de historia regional yde las fronteras. vol. 6, (sept. 2001) ; p. 3 -;5