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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.
3
votes
Accepted
Double duals characteristic
Note that there exists such a $Y$ iff the sequence
$$0\to X\overset{\varphi}{\to} (X^\*)^\*\overset{\eta}{\to} \mathrm{coker}\:\varphi\to 0$$
splits, where $\varphi$ is the canonical injection and $\e …