The distortion of Hilbert space |
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| Authors: | E Odell Th Schlumprecht |
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| Institution: | (1) Department of Mathematics, The University of Texas at Austin, 78712-1082 Austin, TX, USA;(2) Department of Mathematics, Louisiana State University, 70803 Baton Rouge, LA, USA;(3) Present address: Department of Mathematics, Texas A&M University, 77843 College Station, TX, USA |
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| Abstract: | The unit sphere of Hilbert space,  2, is shown to contain a remarkable sequence of nearly orthogonal sets. Precisely, there exist a sequence of sets of norm one elements of 2, (C
i
)
i=1
, and reals 
i
 0 so that a) each setC
i
has nonempty intersection with every infinite dimensional closed subspace of 2 and b) fori j,x C, andyC
j
, | x, y |<min(i, j)
E. Odell was partially supported by NSF and TARP. Th. Schlumprecht was partially supported by NSF and LEQSF. |
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| Keywords: | Primary 46C05 Secondary 46B03 46B20 46B42 |
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