Classical Banach spaces |
| Dual space | Reflexive | weakly sequentially complete | Norm | Notes |
| | Yes | Yes | | | Euclidean space |
| | Yes | Yes | | | |
| | Yes | Yes | | | |
| | Yes | Yes | | | |
| | No | Yes | | | |
| | No | No | | | |
| | No | No | | | |
| | No | No | | | Isomorphic but not isometric to |
| | No | Yes | | | Isometrically isomorphic to |
| | No | Yes | | | Isometrically isomorphic to |
| | No | No | | | Isometrically isomorphic to |
| | No | No | | | Isometrically isomorphic to |
| | No | No | | | |
| | No | No | | | |
| ? | No | Yes | | | |
| ? | No | Yes | | | A closed subspace of |
| ? | No | Yes | | | A closed subspace of |
| | Yes | Yes | | | |
| | No | Yes | | | The dual is if is -finite. |
| ? | No | Yes | | | is the total variation of |
| ? | No | Yes | | | consists of functions such that |
| | No | Yes | | | Isomorphic to the Sobolev space |
| | No | No | | | Isomorphic to essentially by Taylor's theorem. |