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Suppose that $K_{1}$ and $K_{2}$ are pointed closed cones in a finite-dimensional space $V$ whose Hilbert metrics $d_{1},d_{2}$ are known. Is there a way to express the Hilbert metric of $K_{1}+K_{2}$ in terms of $d_{1}$ and $d_{2}$?

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Do you mean the Hilbert projective metric? –  Suvrit Sep 30 '13 at 14:20
What exactly do you mean by "the Hilbert metric"? –  Rami Oct 3 '13 at 15:50
@suv....rit Sure –  Felix Goldberg Oct 4 '13 at 18:32

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