dc.creator | Andruchow, Esteban | |
dc.date.accessioned | 2022-01-12T19:23:26Z | |
dc.date.accessioned | 2022-10-14T22:03:24Z | |
dc.date.available | 2022-01-12T19:23:26Z | |
dc.date.available | 2022-10-14T22:03:24Z | |
dc.date.created | 2022-01-12T19:23:26Z | |
dc.date.issued | 2021-07 | |
dc.identifier | Andruchow, Esteban; Geodesics of projections in von neumann algebras; American Mathematical Society; Proceedings of the American Mathematical Society; 149; 10; 7-2021; 4501-4513 | |
dc.identifier | 0002-9939 | |
dc.identifier | http://hdl.handle.net/11336/150001 | |
dc.identifier | 1088-6826 | |
dc.identifier | CONICET Digital | |
dc.identifier | CONICET | |
dc.identifier.uri | https://repositorioslatinoamericanos.uchile.cl/handle/2250/4311766 | |
dc.description.abstract | Let 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.language | eng | |
dc.publisher | American Mathematical Society | |
dc.relation | info:eu-repo/semantics/altIdentifier/url/https://www.ams.org/proc/2021-149-10/S0002-9939-2021-15568-8/ | |
dc.relation | info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1090/proc/15568 | |
dc.rights | https://creativecommons.org/licenses/by-nc-sa/2.5/ar/ | |
dc.rights | info:eu-repo/semantics/restrictedAccess | |
dc.subject | PROJECTIONS | |
dc.subject | GEODESICS OF PROJECTIONS | |
dc.subject | VON NEUMANN ALGEBRAS | |
dc.subject | INDEX FOR SUBFACTORS | |
dc.title | Geodesics of projections in von neumann algebras | |
dc.type | info:eu-repo/semantics/article | |
dc.type | info:ar-repo/semantics/artículo | |
dc.type | info:eu-repo/semantics/publishedVersion | |