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'Banach spaces with complemented subspaces'
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| Title of object: |
Banach spaces with complemented subspaces |
| Canonical Name: |
CharacterizationOfAHilbertSpace |
| Type: |
Theorem |
| Created on: |
2006-06-27 15:32:30 |
| Modified on: |
2006-11-08 02:11:05 |
| Classification: |
msc:46C15 |
Revision comment (for changes between this and next version):
| Changes for correction #10529 ('wording'). |
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Content:
Theorem. [Lindenstrauss-Tzafriri]
Let $V$ be a Banach space, such that for each closed subspace $M$ there exists a closed subspace $N$ such that $M\cap N=0$ 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). |
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