Definition:Banach Space

From ProofWiki
Jump to navigation Jump to search


A Banach space is a normed vector space where every Cauchy sequence is convergent.

Also known as

A Banach space is also known as a complete normed vector space.


Euclidean Space

A Euclidean space with the usual Euclidean norm is a Banach space.

Square-Integrable Real-Valued Mappings

Let $S$ be the space of all square-integrable real-valued functions.

Then $S$ is a Banach space.

Also see

  • Results about Banach spaces can be found here.

Source of Name

This entry was named for Stefan Banach.