Abstract
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, $n\in \mathbb{n}$.
Citation
Manuel Valdivia. "On certain (LB)-spaces." Bull. Belg. Math. Soc. Simon Stevin 14 (3) 565 - 575, September 2007. https://doi.org/10.36045/bbms/1190994219
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