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Some relations between entropy and approximation numbers

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Abstract

A general result is obtained which relates the entropy numbers of compact maps on Hilbert space to its approximation numbers. Compared with previous works in this area, it is particularly convenient for dealing with the cases where the approximation numbers decay rapidly. A nice estimation between entropy and approximation numbers for noncompact maps is given.

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Authors and Affiliations

  1. School of Mathematical Sciences, Peking University, 100871, Beijing, China

    Zhiming Zheng

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  1. Zhiming Zheng
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Additional information

Partially supported by the National 863 Project of China and the National Natural Science Foundation of China (Grant No. 19771003).

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Zheng, Z. Some relations between entropy and approximation numbers. Sci. China Ser. A-Math. 42, 478–487 (1999). https://doi.org/10.1007/BF02882243

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  • DOI: https://doi.org/10.1007/BF02882243

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