Rate of Decay of the Bernstein Numbers
@inproceedings{Plichko2012RateOD,
title={Rate of Decay of the Bernstein Numbers},
author={Anatolij M. Plichko},
year={2012}
}We show that if a Banach space X contains uniformly complemented `2 ’s then there exists a universal constant b = b(X) > 0 such that for each Banach space Y , and any sequence dn ↓ 0 there is a bounded linear operator T : X → Y with the Bernstein numbers bn(T ) of T satisfying b−1dn ≤ bn(T ) ≤ bdn for all n.
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