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dc.contributor.author
Andruchow, Esteban
dc.contributor.author
Chiumiento, Eduardo Hernan
dc.contributor.author
Di Iorio y Lucero, María Eugenia
dc.date.available
2017-04-07T14:47:00Z
dc.date.issued
2015-01-15
dc.identifier.citation
Andruchow, Esteban; Chiumiento, Eduardo Hernan; Di Iorio y Lucero, María Eugenia; Essentially commuting projections; Elsevier; Journal of Functional Analysis; 268; 2; 15-1-2015; 336-362
dc.identifier.issn
0022-1236
dc.identifier.uri
http://hdl.handle.net/11336/14948
dc.description.abstract
Let H=H+⊕H- be a fixed orthogonal decomposition of a Hilbert space, with both subspaces of infinite dimension, and let E+, E- be the projections onto H+ and H-. We study the set Pcc of orthogonal projections P in H which essentially commute with E+ (or equivalently with E-), i.e.[P,E+]=PE+-E+Pis compact. By means of the projection π onto the Calkin algebra, one sees that these projections P∈Pcc fall into nine classes. Four discrete classes, which correspond to π(P) being 0, 1, π(E+) or π(E-), and five essential classes which we describe below. The discrete classes are, respectively, the finite rank projections, finite co-rank projections, the Sato Grassmannian of H+ and the Sato Grassmannian of H-. Thus the connected components of each of these classes are parametrized by the integers (via de rank, the co-rank or the Fredholm index, respectively). The essential classes are shown to be connected.We are interested in the geometric structure of Pcc, being the set of selfadjoint projections of the C*-algebra Bcc of operators in B(H) which essentially commute with E+. In particular, we study the problem of existence of minimal geodesics joining two given projections in the same component. We show that the Hopf-Rinow Theorem holds in the discrete classes, but not in the essential classes. Conditions for the existence and uniqueness of geodesics in these latter classes are found.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Elsevier
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.subject
Projections
dc.subject
Compact Operators
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Fredholm Index
dc.subject
Geodesics
dc.subject.classification
Matemática Pura
dc.subject.classification
Matemáticas
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
dc.title
Essentially commuting projections
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2015-10-29T15:07:03Z
dc.journal.volume
268
dc.journal.number
2
dc.journal.pagination
336-362
dc.journal.pais
Países Bajos
dc.journal.ciudad
Amsterdam
dc.description.fil
Fil: Andruchow, Esteban. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemáticas; Argentina. Universidad Nacional de General Sarmiento; Argentina
dc.description.fil
Fil: Chiumiento, Eduardo Hernan. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemáticas; Argentina. Universidad Nacional de La Plata. Facultad de Cencias Económicas; Argentina
dc.description.fil
Fil: Di Iorio y Lucero, María Eugenia. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemáticas; Argentina. Universidad Nacional de General Sarmiento; Argentina
dc.journal.title
Journal of Functional Analysis
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/http://www.sciencedirect.com/science/article/pii/S0022123614004169
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1016/j.jfa.2014.10.003
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