Subspace Condition for Bernstein's Lethargy Theorem

@article{Aksoy2016SubspaceCF,
  title={Subspace Condition for Bernstein's Lethargy Theorem},
  author={Asuman G{\"u}ven Aksoy and Monairah Al-Ansari and Caleb Case and Qidi Peng},
  journal={arXiv: Functional Analysis},
  year={2016}
}
In this paper, we consider a condition on subspaces in order to improve bounds given in the Bernstein's Lethargy Theorem (BLT) for Banach spaces. Let $d_1 \geq d_2 \geq \dots d_n \geq \dots > 0$ be an infinite sequence of numbers converging to $0$, and let $Y_1 \subset Y_2 \subset \dots\subset Y_n \subset \dots \subset X$ be a sequence of closed nested subspaces in a Banach space $X$ with the property that $\overline{Y}_{n}\subset Y_{n+1}$ for all $n\ge1$. We prove that for any $c \in (0,1… 

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