Banach space

Definition

A Banach space is a complete vector space $B$ with a norm $\lVert \cdot \rVert$

(i.e., a normed vector space $B$ where every Cauchy sequence in $B$ converges)

Notes

• Lp space is a typical example of a Banach space

References

1. https://mathworld.wolfram.com/BanachSpace.html
2. https://e.math.cornell.edu/people/belk/measuretheory/BanachSpaces.pdf
3. https://en.wikipedia.org/wiki/Banach_space