Edward Odell worked on the geometry of Banach spaces. With Thomas Schlumprecht, he solved the distortion problem for the classical infinite-dimensional Hilbert space by proving it arbitrarily distortable.[ref]
The distortion problem by Edward Odell and Thomas Schlumprecht. Original byline and introduction
An equivalent norm can preserve the underlying vector-space topology yet stretch unit vectors very differently inside every infinite-dimensional subspace. For any prescribed ratio greater than one, their construction forces such variation. This distinguishes topological equivalence of norms from uniform control of their geometry on large subspaces.[ref]
