Banach spaces with complemented subspaces

Theorem. [Lindenstrauss-Tzafriri]

Let V be a Banach spaceMathworldPlanetmath, such that for each closed subspace M there exists a closed subspace N such that MN=0 and M+N=V (i.e. every closed subspace is complemented). Then V is isomorphic to a Hilbert spaceMathworldPlanetmath (i.e. there exists a Hilbert space structure on V that induces the original topologyMathworldPlanetmath 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