On the topology of pointwise convergence on the boundaries of 𝐿₁-preduals

Moors, Warren; Spurný, Jiří

doi:10.1090/S0002-9939-08-09708-6

On the topology of pointwise convergence on the boundaries of $L_1$-preduals
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by Warren B. Moors and Jiří Spurný PDF

Proc. Amer. Math. Soc. 137 (2009), 1421-1429 Request permission

Abstract:

In this paper we prove a theorem more general than the following: “If $(X,\|\cdot \|)$ is an $L_1$-predual, $B$ is any boundary of $X$ and $\{x_n:n \in \mathbb {N} \}$ is any subset of $X$, then the closure of $\{x_n:n \in \mathbb {N} \}$ with respect to the topology of pointwise convergence on $B$ is separable with respect to the topology generated by the norm, whenever $\textrm {Ext}(B_{X^*})$ is weak$^*$ Lindelöf.” Several applications of this result are also presented.

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