The Lindenstrauss-Tzafriri theorem and the local theory of Banach spaces

Let $X$ be a Banach space. The Lindenstaruss-Tzafriri theorem states that if each closed subspace of $X$ is complemented in $X$, then $X$ is topologically isomorphic to a Hilbert space. It turns out that the above result can be equivalently stated in terms of finite-dimensional subspaces of $X$, and that it can be proved with the help of the local theory of Banach spaces. In my talk, I am going to present such a proof.