Inequalities between Entropy and Approximation Numbers of Compact Maps

R.M. Edmunds

doi:10.4171/zaa/299

JournalszaaVol. 7, No. 3pp. 223–227

Inequalities between Entropy and Approximation Numbers of Compact Maps

R.M. Edmunds
University College, Cardiff, UK

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Abstract

It is shown that if $T$ is a compact linear map, with infinite-dimensional range, from one Hilbert space to another, then given any $N \in N, e_{n} (T) \leq 2 a_{N + 1} (T)$ for any $n$ satisfying a certain inequality. Applications of this are given.

Cite this article

R.M. Edmunds, Inequalities between Entropy and Approximation Numbers of Compact Maps. Z. Anal. Anwend. 7 (1988), no. 3, pp. 223–227

DOI 10.4171/ZAA/299