Abstract
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, (C i ) ∞ i=1 , and reals ε i ↓0 so that a) each setC i has nonempty intersection with every infinite dimensional closed subspace of ℓ2 and b) fori≠j,x∈C, andy∈C j , |〈x, y〉|<εmin(i, j)
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E. Odell was partially supported by NSF and TARP. Th. Schlumprecht was partially supported by NSF and LEQSF.
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Odell, E., Schlumprecht, T. The distortion of Hilbert space. Geometric and Functional Analysis 3, 201–207 (1993). https://doi.org/10.1007/BF01896023
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DOI: https://doi.org/10.1007/BF01896023