dc.creatorAndruchow, Esteban
dc.date.accessioned2022-01-12T19:23:26Z
dc.date.accessioned2022-10-14T22:03:24Z
dc.date.available2022-01-12T19:23:26Z
dc.date.available2022-10-14T22:03:24Z
dc.date.created2022-01-12T19:23:26Z
dc.date.issued2021-07
dc.identifierAndruchow, Esteban; Geodesics of projections in von neumann algebras; American Mathematical Society; Proceedings of the American Mathematical Society; 149; 10; 7-2021; 4501-4513
dc.identifier0002-9939
dc.identifierhttp://hdl.handle.net/11336/150001
dc.identifier1088-6826
dc.identifierCONICET Digital
dc.identifierCONICET
dc.identifier.urihttps://repositorioslatinoamericanos.uchile.cl/handle/2250/4311766
dc.description.abstractLet A be a von Neumann algebra and PA the manifold of projections in A. There is a natural linear connection in PA, which in the finite dimensional case coincides with the the Levi-Civita connection of the Grassmann manifold of Cn. In this paper we show that two projections p, q can be joined by a geodesic, which has minimal length (with respect to the metric given by the usual norm of A), if and only if p ∧ q⊥ ∼ p⊥ ∧ q, where ∼ stands for the Murray-von Neumann equivalence of projections. It is shown that the minimal geodesic is unique if and only if p ∧ q⊥ = p⊥ ∧ q = 0. If A is a finite factor, any pair of projections in the same connected component of PA (i.e., with the same trace) can be joined by a minimal geodesic. We explore certain relations with Jones’ index theory for subfactors. For instance, it is shown that if N ⊂M are II1 factors with finite index [M : N ] = t−1, then the geodesic distance d(eN , eM) between the induced projections eN and eM is d(eN , eM) = arccos(t1/2).
dc.languageeng
dc.publisherAmerican Mathematical Society
dc.relationinfo:eu-repo/semantics/altIdentifier/url/https://www.ams.org/proc/2021-149-10/S0002-9939-2021-15568-8/
dc.relationinfo:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1090/proc/15568
dc.rightshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.rightsinfo:eu-repo/semantics/restrictedAccess
dc.subjectPROJECTIONS
dc.subjectGEODESICS OF PROJECTIONS
dc.subjectVON NEUMANN ALGEBRAS
dc.subjectINDEX FOR SUBFACTORS
dc.titleGeodesics of projections in von neumann algebras
dc.typeinfo:eu-repo/semantics/article
dc.typeinfo:ar-repo/semantics/artículo
dc.typeinfo:eu-repo/semantics/publishedVersion


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