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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$\begingroup$ Do you mean the Hilbert projective metric? $\endgroup$– SuvritSep 30, 2013 at 14:20
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$\begingroup$ What exactly do you mean by "the Hilbert metric"? $\endgroup$– RamiOct 3, 2013 at 15:50
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$\begingroup$ @suv....rit Sure $\endgroup$– Felix GoldbergOct 4, 2013 at 18:32
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