On certain (LB)-spaces
Valdivia, Manuel
Bull. Belg. Math. Soc. Simon Stevin, Tome 13 (2007) no. 5, p. 565-575 / Harvested from Project Euclid
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Let $(X_n)$ be a sequence of infinite-dimensional Banach spaces. For $E$ being the space $\bigoplus_{n=1}^\infty X_n$, the following equivalences are shown: 1. $E' [\mu(E',E)]$ is B-complete. 2. Every separated quotient of $E' [\mu(E',E)]$ is complete. 3. Every separated quotient of $E$ satisfies Mackey's weak condition. 4. $X_n$ is quasi-reflexive, $n\in \mathbb{n}$.
Publié le : 2007-09-14
Classification:  46 A 13,  46 A 04 
@article{1190994219,
     author = {Valdivia, Manuel},
     title = {On certain (LB)-spaces},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {13},
     number = {5},
     year = {2007},
     pages = { 565-575},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1190994219}
}

Valdivia, Manuel. On certain (LB)-spaces. Bull. Belg. Math. Soc. Simon Stevin, Tome 13 (2007) no. 5, pp.  565-575. http://gdmltest.u-ga.fr/item/1190994219/