## Bulletin of the Belgian Mathematical Society - Simon Stevin

### On certain (LB)-spaces

Manuel Valdivia

#### 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, $n\in \mathbb{n}$.

#### Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 14, Number 3 (2007), 565-575.

Dates
First available in Project Euclid: 28 September 2007

https://projecteuclid.org/euclid.bbms/1190994219

Digital Object Identifier
doi:10.36045/bbms/1190994219

Mathematical Reviews number (MathSciNet)
MR2387055

Zentralblatt MATH identifier
1133.46003

Subjects
Primary: 46 A 13
Secondary: 46 A 04

#### Citation

Valdivia, Manuel. On certain (LB)-spaces. Bull. Belg. Math. Soc. Simon Stevin 14 (2007), no. 3, 565--575. doi:10.36045/bbms/1190994219. https://projecteuclid.org/euclid.bbms/1190994219