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math.FA1999
John decompositions: selecting a large part
R. Vershynin
We extend the invertibility principle of J. Bourgain and L. Tzafriri to operators acting on arbitrary decompositions id = \sum x_j \otimes x_j, rather than on the coordinate one. T…
math.FA1999
Subsequences of frames
R. Vershynin
Every frame in Hilbert space contains a subsequence equivalent to an orthogonal basis. If a frame is n-dimensional then this subsequence has length (1 - ε) n. On the other hand, th…