Banach limit in convexity and geometric means for convex bodies

Liran  Rotem

doi:10.3934/era.2016.23.005

Article Contents

2016, Volume 23: 41-51. Doi: 10.3934/era.2016.23.005

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Banach limit in convexity and geometric means for convex bodies

Liran Rotem^1,

1.
University of Minnesota, School of Mathematics

Received: July 31, 2016

Revised: September 30, 2016

Published: December 2015

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Abstract

In this note we construct Banach limits on the class of sequences of convex bodies. Surprisingly, the construction uses the recently introduced geometric mean of convex bodies. In the opposite direction, we explain how Banach limits can be used to construct a new variant of the geometric mean that has some desirable properties.

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Mathematics Subject Classification: 52A20, 46A22.

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References

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