Entropy extension

We prove an “entropy extension-lifting theorem.” It consists of two inequalities for the covering numbers of two symmetric convex bodies. The first inequality, which can be called an “entropy extension theorem,” provides estimates in terms of entropy of sections and should be compared with the exten...

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Veröffentlicht in:	Functional analysis and its applications 2006-10, Vol.40 (4), p.298-303, Article 65
Hauptverfasser:	Litvak, A. E., Milman, V. D., Pajor, A., Tomczak-Jaegermann, N.
Format:	Artikel
Sprache:	eng
Schlagworte:	Entropy Estimates Theorems
Online-Zugang:	Volltext
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Zusammenfassung:	We prove an “entropy extension-lifting theorem.” It consists of two inequalities for the covering numbers of two symmetric convex bodies. The first inequality, which can be called an “entropy extension theorem,” provides estimates in terms of entropy of sections and should be compared with the extension property of ℓ∞. The second one, which can be called an “entropy lifting theorem,” provides estimates in terms of entropies of projections.
ISSN:	0374-1990 0016-2663 1573-8485
DOI:	10.1007/s10688-006-0046-8