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Paper detail

A dual formula for the spectral distance in noncommutative geometry

In noncommutative geometry, Connes's spectral distance is an extended metric on the state space of a C*-algebra generalizing Kantorovich's dual formula of the Wasserstein distance of order 1 from optimal transport. It is expressed as a supremum. We present a dual formula - as an infimum - generalizing Beckmann's "dual of the dual" formulation of the Wasserstein distance. We then discuss some examples with matrix algebras, where such a dual formula may be useful to obtain upper bounds for the distance.

preprint2020arXivOpen access
Francesco D'AndreaPierre Martinetti
math.OAmath-phmath.MP
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Francesco D'AndreaPierre Martinetti

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