Banach Spaces
Definition
Examples
Example 1: and with any norm (finite-dimensional)
Example 2: with for
Example 3: with
Example 4: with
Example 5: with
Importance
Key Theorems
Baire Category Theorem
Uniform Boundedness Principle
If is a family of bounded linear operators from a Banach space to a normed space with for each , then .
Open Mapping Theorem
Closed Graph Theorem
Hahn-Banach Theorem
Banach Algebras
Spectral Theory
Examples of Banach Spaces
Separable Banach Spaces
and () are separable. is not.