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arXiv · 1807.06935

A dual formula for the spectral distance in noncommutative geometry

Francesco D'Andrea·Pierre Martinetti
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Abstract

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.

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Francesco D'Andrea, Pierre Martinetti. 2018-07-18. A dual formula for the spectral distance in noncommutative geometry. https://doi.org/10.1016/j.geomphys.2020.103920

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