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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.

1 vote

Unbounded operator bounded in a dense subset

This is just to make Nate Eldridge's answer selfcontained. For any normed vector space $V$ and any $r > 0$, write $V_r$ for the open ball of radius $r$ and center $0$ in $V$. Let $X$ be a normed vec …
Pierre-Yves Gaillard's user avatar