On the Hilbert geometry of products

Vernicos, Constantin

doi:10.1090/S0002-9939-2015-12504-X

On the Hilbert geometry of products
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Proc. Amer. Math. Soc. 143 (2015), 3111-3121 Request permission

Abstract:

We prove that the Hilbert geometry of a product of convex sets is bi-lipschitz equivalent to the direct product of their respective Hilbert geometries. We also prove that the volume entropy is additive with respect to product and that amenability of a product is equivalent to the amenability of each term.

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