Journal Article

Geometric interpolation of entropy numbers

Radosław Szwedek

in The Quarterly Journal of Mathematics

Volume 69, issue 2, pages 377-389
Published in print June 2018 | ISSN: 0033-5606
Published online September 2017 | e-ISSN: 1464-3847 | DOI: https://dx.doi.org/10.1093/qmath/hax044
Geometric interpolation of entropy numbers

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Abstract

We investigate whether the entropy numbers of an operator behave well under the complex interpolation between Hilbert spaces. We study geometric interpolation of entropy numbers of operators. We deliver a contribution to this problem by showing that an interpolation type inequality holds for these numbers. This is in contrast to the situation in Banach spaces, where by examples of Edmunds and Netrusov the entropy numbers do not interpolate well at least in the situation of the real method. As an application, we also present an interpolation estimate of single eigenvalues by single entropy numbers.

Journal Article.  7661 words. 

Subjects: Pure Mathematics

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