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Joined 2026-09-21 Message
Incoming links: Edward Odell
Edward Odell 2026-11-05
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]
Thomas Schlumprecht 2026-11-05
Thomas Schlumprecht studies the theory of Banach spaces. His joint work with Edward Odell proved arbitrary distortion of infinite-dimensional Hilbert space.[ref]
The distortion problem by Edward Odell and Thomas Schlumprecht. Original byline and introduction
For each chosen distortion threshold, one constructs an equivalent norm whose variation cannot be avoided by passing to any infinite-dimensional subspace. The same threshold need not describe a single norm for every possible ratio: the norm is chosen after the desired ratio. This quantifier order is central to the result and to the notion of bounded distortion of a Banach space.[ref]