Banach spaces with complemented subspaces
Theorem. [Lindenstrauss-Tzafriri]
Let V be a Banach space
, such that for each closed subspace M there exists a closed subspace N such that M∩N=0 and M+N=V (i.e. every closed subspace is complemented). Then V is isomorphic to a Hilbert space
(i.e. there exists a Hilbert space structure on V that induces the original topology
on V as a Banach space).
| Title | Banach spaces with complemented subspaces |
|---|---|
| Canonical name | BanachSpacesWithComplementedSubspaces |
| Date of creation | 2013-03-22 16:02:59 |
| Last modified on | 2013-03-22 16:02:59 |
| Owner | aube (13953) |
| Last modified by | aube (13953) |
| Numerical id | 13 |
| Author | aube (13953) |
| Entry type | Theorem |
| Classification | msc 46C15 |
| Synonym | Lindenstrauss-Tzafriri theorem |
| Synonym | Lindenstrauss-Tzafriri complemented subspace theorem |