A dual formula for the spectral distance in noncommutative geometry

JOURNAL OF GEOMETRY AND PHYSICS

卷:159

Article

D'Andrea, Francesco^1,2  Martinetti, Pierre^3,4 

[1] Univ Napoli Federico II, Complesso MSA,Via Cintia, I-80126 Naples, Italy

[2] Ist Nazl Fis Nucl, Sez Napoli, Complesso MSA,Via Cintia, I-80126 Naples, Italy

[3] Univ Genova DIMA, Via Dodecaneso 35, I-16146 Genoa, Italy

[4] Ist Nazl Fis Nucl, Sez Genova, Via Dodecaneso 35, I-16146 Genoa, Italy

关键词: Spectral triples;    Connes' distance;    Beckmann's problem;   

DOI  :  10.1016/j.geomphys.2020.103920

来源: Elsevier

【 摘 要 】

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 dualformulation 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. (c) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free