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]
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