Mostrar el registro sencillo del ítem
dc.contributor.author
Antezana, Jorge Abel
dc.contributor.author
Ghiglioni, Eduardo Mario
dc.contributor.author
Stojanoff, Demetrio
dc.date.available
2020-05-26T19:44:50Z
dc.date.issued
2020-03
dc.identifier.citation
Antezana, Jorge Abel; Ghiglioni, Eduardo Mario; Stojanoff, Demetrio; Minimal curves in U(n) and Gl(n)+ with respect to the spectral and the trace norms; Academic Press Inc Elsevier Science; Journal of Mathematical Analysis and Applications; 483; 2; 3-2020; 1-26
dc.identifier.issn
0022-247X
dc.identifier.uri
http://hdl.handle.net/11336/105930
dc.description.abstract
Consider the Lie group of n×n complex unitary matrices U(n) endowed with the bi-invariant Finsler metric given by the spectral norm, ‖X‖_U=‖U⁎X‖∞=‖X‖∞ for any X tangent to a unitary operator U. Given two points in U(n), in general there exist infinitely many curves of minimal length. In this paper we provide a complete description of such curves and as a consequence we give an equivalent condition for uniqueness. Similar studies are done for the Grassmann manifolds. On the other hand, consider the cone of n×n positive invertible matrices Gl(n)+ endowed with the bi-invariant Finsler metric given by the trace norm, ‖X‖_1,A = ‖A^−1/2XA^−1/2‖_1 for any X tangent to A∈Gl(n)^+. In this context, also exist infinitely many curves of minimal length. In this paper we provide a complete description of such curves proving first a characterization of the minimal curves joining two Hermitian matrices X,Y∈H(n). The last description is also used to construct minimal paths in the group of unitary matrices U(n) endowed with the bi-invariant Finsler metric ‖X‖_1,U = ‖U⁎X‖_1=‖X‖_1 for any X tangent to U∈U(n). We also study the set of intermediate points in all the previous contexts.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
Academic Press Inc Elsevier Science
dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-nd/2.5/ar/
dc.subject
MINIMAL CURVES
dc.subject
FINSLER METRICS
dc.subject
UNITARY OPERATORS
dc.subject
POSITIVE OPERATORS
dc.subject
GRASSMANN MANIFOLD
dc.subject
INTERMEDIATE POINTS
dc.subject.classification
Matemática Pura
dc.subject.classification
Matemáticas
dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
dc.title
Minimal curves in U(n) and Gl(n)+ with respect to the spectral and the trace norms
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2020-05-19T19:38:19Z
dc.identifier.eissn
1096-0813
dc.journal.volume
483
dc.journal.number
2
dc.journal.pagination
1-26
dc.journal.pais
Estados Unidos
dc.description.fil
Fil: Antezana, Jorge Abel. Universidad Nacional de La Plata; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
dc.description.fil
Fil: Ghiglioni, Eduardo Mario. Universidad Nacional de La Plata; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
dc.description.fil
Fil: Stojanoff, Demetrio. Universidad Nacional de La Plata; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Instituto Argentino de Matemática Alberto Calderón; Argentina
dc.journal.title
Journal of Mathematical Analysis and Applications
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/https://doi.org/10.1016/j.jmaa.2019.123632
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/arxiv/https://arxiv.org/abs/1907.03368
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://www.sciencedirect.com/science/article/abs/pii/S0022247X1930900X
Archivos asociados