Theorem 12.6.13 (Lindenstrauss-Tzafriri, 1971).label Let $E$ be a Banach space. If for every closed subspace $A \subset E$, there exists a closed subspace $A^{\perp} \subset E$ such that $E = A \oplus A^{\perp}$, then $E$ is isomorphic to a Hilbert space.