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dc.date.accessioned 2019-11-08T16:40:07Z
dc.date.available 2019-11-08T16:40:07Z
dc.date.issued 2014
dc.identifier.uri http://sedici.unlp.edu.ar/handle/10915/85244
dc.description.abstract Let A be a positive injective operator in a Hilbert space (H,〈{dot operator},{dot operator}〉), and denote by [ {dot operator}, {dot operator} ] the inner product defined by A: [f, g] = 〈A f, g〉. A closed subspace S⊂H is called A-compatible if there exists a closed complement for S, which is orthogonal to S with respect to the inner product [ {dot operator}, {dot operator} ]. Equivalently, if there exists a necessarily unique bounded idempotent operator QS such that R(QS)=S, which is symmetric for this inner product. The compatible Grassmannian Gr A is the set of all A-compatible subspaces of H. By parametrizing it via the one to one correspondence S↔QS, this set is shown to be a differentiable submanifold of the Banach space of all bounded operators in H which are symmetric with respect to the form [ {dot operator}, {dot operator} ]. A Banach-Lie group acts naturally on the compatible Grassmannian, the group of all invertible operators in H which preserve the form [ {dot operator}, {dot operator} ]. Each connected component in Gr A of a compatible subspace S of finite dimension, turns out to be a symplectic leaf in a Banach Lie-Poisson space. For 1 ≤ p ≤ ∞, in the presence of a fixed [ {dot operator}, {dot operator} ]-orthogonal (direct sum) decomposition of H, H=S0+N0, we study the restricted compatible Grassmannian (an analogue of the restricted, or Sato Grassmannian). This restricted compatible Grassmannian is shown to be a submanifold of the Banach space of p-Schatten operators which are symmetric for the form [ {dot operator}, {dot operator} ]. It carries the locally transitive action of the Banach-Lie group of invertible operators which preserve [ {dot operator}, {dot operator} ], and are of the form G = 1 + K, with K in the p-Schatten class. The connected components of this restricted Grassmannian are characterized by means of the Fredholm index of pairs of projections. Finsler metrics which are isometric for the group actions are introduced for both compatible Grassmannians, and minimality results for curves are proved. en
dc.format.extent 1-27 es
dc.language en es
dc.subject Compatible subspace es
dc.subject Grassmannian es
dc.subject Restricted Grassmannian es
dc.title The compatible Grassmannian en
dc.type Articulo es
sedici.identifier.other doi:10.1016/j.difgeo.2013.11.004 es
sedici.identifier.other eid:2-s2.0-84887694168 es
sedici.identifier.issn 0926-2245 es
sedici.creator.person Andruchow, Esteban es
sedici.creator.person Chiumiento, Eduardo H. es
sedici.creator.person Di Iorio y Lucero, M. E. es
sedici.subject.materias Matemática es
sedici.description.fulltext true es
mods.originInfo.place Facultad de Ciencias Exactas es
sedici.subtype Articulo es
sedici.rights.license Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
sedici.rights.uri http://creativecommons.org/licenses/by-nc-sa/4.0/
sedici.description.peerReview peer-review es
sedici.relation.journalTitle Differential Geometry and its Application es
sedici.relation.journalVolumeAndIssue vol. 32, no. 1 es
sedici.rights.sherpa * Color: green * Pre-print del autor: si * Post-print del autor: si * Versión de editor/PDF:no * Condiciones: >>Authors pre-print on any website, including arXiv and RePEC >>Author's post-print on author's personal website immediately >>Author's post-print on open access repository after an embargo period of between 12 months and 48 months >>Permitted deposit due to Funding Body, Institutional and Governmental policy or mandate, may be required to comply with embargo periods of 12 months to 48 months >>Author's post-print may be used to update arXiv and RepEC >>Publisher's version/PDF no be used >>Must link to publisher version with DOI >>Author's post-print must be released with a Creative Commons Attribution Non-Commercial No Derivatives License >>Publisher last reviewed on 03/06/2015 * Link a Sherpa: http://sherpa.ac.uk/romeo/issn/0926-2245/es/


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Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) Except where otherwise noted, this item's license is described as Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)