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arXiv · 1903.00541

Some New Bounds on the Entropy Numbers of Diagonal Operators

Simon Fischer
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Abstract

Entropy numbers are an important tool for quantifying the compactness of operators. Besides establishing new upper bounds on the entropy numbers of diagonal operators $D_\sigma$ from $\ell_p$ to $\ell_q$, where $p\not=q$, we investigate the optimality of these bounds. In case of $p q$ we show optimality under weaker assumption than previously used in the literature. In addition, we illustrate the benefit of our results with examples not covered in the literature so far.

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BibTeXRIS

Simon Fischer. 2019-03-01. Some New Bounds on the Entropy Numbers of Diagonal Operators. https://doi.org/10.1016/j.jat.2019.105343

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