# 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.

## 6 Citations

### On Shapiro's lethargy theorem and some applications

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### Subspace Condition for Bernstein's Lethargy Theorem

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Abstract give estimates for the approximation numbers of composition operators on the Hp spaces, 1 ≤ p < ∞

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