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A Banach space is a complete normed vector space: A vector space equipped with a norm such that every Cauchy sequence converges.

7 votes
2 answers
801 views

Is a subspace with a certain property dense in the dual of a vector space?

Suppose we have a normed vector space $V$ and its dual $V^*$, and suppose that $X \subseteq V^*$ has the property that for every $v \in V$, there is some $\phi \in X$ with $\Vert \phi \Vert = 1$ such …
Alden Walker's user avatar