Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some New Bounds on the Entropy Numbers of Diagonal Operators   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 $p<q$ optimality is
proven for fast decaying diagonal sequences, which include exponentially
decreasing sequences. 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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The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
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The categories of this paper are: eess
20
The categories of this paper are: acc-phys
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-th
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The categories of this paper are: cs
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ex
3
The categories of this paper are: physics
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The categories of this paper are: q-fin
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The categories of this paper are: econ
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The categories of this paper are: quant-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: mtrl-th