Answer by Nate Eldredge for Banach-Alaoglu theorem and coarseness of weak...
of course $D$ is compact in the norm topologyThat is your error. When $X$ is infinite dimensional, $D$ is not compact in the norm topology.The norm topology on $X^*$ is always at least as fine (strong)...
View ArticleBanach-Alaoglu theorem and coarseness of weak star topology
Let $X$ be a normed space and let $X^\ast$ denote its continuous dual. There is a norm on $X^\ast$ defined by $\|\varphi\|=\sup_{\|x\|=1}|\varphi(x)|$. The weak star topology on $X^\ast$ is defined to...
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