The distortion of Hilbert space
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The unit sphere of Hilbert space, ℓ2, is shown to contain a remarkable sequence of nearly orthogonal sets. Precisely, there exist a sequence of sets of norm one elements of ℓ2, (Ci)i=1∞, and reals εi↓0 so that a) each set Ci has nonempty intersection with every infinite dimensional closed subspace of ℓ2 and b) for i≠j, x∈C, and y∈Cj, |〈x, y〉|<εmin(i, j) © 1993 Birkhäuser Verlag.
author list (cited authors)
Odell, E., & Schlumprecht, T. h.