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We prove an analogous of Banach Theorem for approximativelysurjective mappings on Schwartz b-spaces associated to Frechetspaces.

Tipo de documento: Artículo - Article

Palabras clave: Approximatively surjective mapping, Schwartz b-space.





Source: http://www.bdigital.unal.edu.co


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Boletı́n de Matemáticas Nueva Serie, Volumen XIV No.
1 (2007), pp.
64–67 BANACH THEOREM FOR APPROXIMATIVELY SURJECTIVE MAPPINGS BELMESNAOUI AQZZOUZ (*) REDOUANE NOUIRA (**) Abstract.
We prove an analogous of Banach Theorem for approximatively surjective mappings on Schwartz b-spaces associated to Fréchet spaces. Key Words and Phrases. Approximatively surjective mapping, Schwartz b-space. Resumen.
Se prueba un resultado análogo al Teorema de Banach para funciones aproximadamente sobreyectivas sobre b-espacios de Schwartz asociados a espacios de Fréchet. Palabras claves.
Función aproximadamente sobreyectiva, b-espacios de Schwartz 2000 Mathematics Subject Classification: 46M05, 46M15, 46M40. 1.
Introduction and notations On the category of Fréchet spaces (i.e.
complete and metrizable locally convex spaces) and continuous linear mappings Fré, the projective limit is a left exact functor which is not necessary right exact.
But Mittag-Leffler Lemma gave a sufficient condition in order that the projective limit functor be exact ([7], p.
23).
In this Lemma, the morphisms of the projective system considered are mappings with a dense range.
We will use the bornological property, and we call mappings which satisfy such condition approximatively surjective mappings. In the Banach case (and in the Fréchet case) it is clear that a mapping is (*) Belmesnaoui AQZZOUZ, Université Mohammed V-Souissi, Faculté des Sciences Economiques, Juridiques et Sociales, Département d’Economie, B.P.
5295, Sala Eljadida, Morocco.
E-mail: baqzzouz@hotmail.com (**) Redouane NOUIRA, Université Ibn Tofail, Faculté des Sciences, Département de Mathématiques, B.P.
133, Kénitra, Morocco. 64 BANACH THEOREM FOR APPROXIMATIVELY SURJECTIVE MAPPINGS 65 approximatively surjective if and only if it has a dense range.
Let us remark that Hörmander ([3], p.
44) used such Lemma in the Remark after Corollary 10.6.10. On the other hand, the Banach Theorem says that if ...






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