Chapter

Geometric Aspects of Functional Analysis

Volume 1317 of the series Lecture Notes in Mathematics pp 224-231

Date:

Some remarks on the geometry of convex sets

  • Keith BallAffiliated withDepartment of Pure Mathematics and Mathematical Statistics, Cambridge University

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Abstract

We prove a strengthening of Santalo's inequality for the unit balls of normed spaces with 1-unconditional bases and observe that all central sections of the unit cube in R n (for n ≥ 10) have smaller volume than those of the Euclidean ball of volume 1.