On strong duals of uniformly λ(P)-nuclear spaces

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On strong duals of uniformly λ(P)-nuclear spaces

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Title: On strong duals of uniformly λ(P)-nuclear spaces
Author: García Lafuente, José María
Abstract: Smooth sequence spaces λ(P) of infinite type of G∞-Spaces were introduced in [7] by Terzioglu as a generalization of power series spaces λ(α) of infinite type. The corresponding study of λ(P)-nuclearity is carried out in [6], extending the notion of λ(α)-nuclearity of Ramanujan. ([5]). In the present paper we give a condition on P and P´ for a Köthe space uniformily λ(P)-nuclear has a strong dual λ(P´)-nuclear, where λ(P) and λ(P´) are nuclear G∞-Spaces. From this result one can deduce a condition, already known by Ramanujan ([5]), about Λ(α)-nuclearity of strong duals.Los espacios de secuencia suaves Λ(P) de tipo infinito de G∞-Espacios fueron introducidas en [7] por Terzioglu como una generalización de λ espacios de series de potencias (α) de tipo infinito. El estudio correspondiente de λ(P)-nuclear se lleva a cabo en [6] , extendiendo la noción de λ (α)-nuclear de Ramanujan ([5]). En el presente trabajo se da una condición de P y P' para un espacio Köthe uniforme λ(P)-nuclear teniendo un dual fuerte λ(P') nuclear, donde λ(P) y λ (P') son espacios G∞ nucleares. De este resultado se puede deducir una condición, ya conocida por Ramanujan ([5]) , sobre Λ(α)-nuclear de duales fuertes.
URI: http://hdl.handle.net/10662/4457
Date: 1987


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