dc.contributor.author |
Corach, G. |
dc.contributor.author |
Maestripieri, Alejandra |
dc.date |
2010 |
dc.identifier |
https://ddd.uab.cat/record/57605 |
dc.identifier |
urn:10.5565/PUBLMAT_54210_09 |
dc.identifier |
urn:oai:ddd.uab.cat:57605 |
dc.identifier |
urn:oai:raco.cat:article/191393 |
dc.identifier |
urn:scopus_id:78249242724 |
dc.identifier |
urn:wos_id:000280567900009 |
dc.identifier |
urn:articleid:20144350v54n2p461 |
dc.format |
application/pdf |
dc.language |
eng |
dc.publisher |
|
dc.relation |
Publicacions matemàtiques ; Vol. 54, Núm. 2 (2010), p. 461-484 |
dc.rights |
open access |
dc.rights |
Tots els drets reservats. |
dc.rights |
https://rightsstatements.org/vocab/InC/1.0/ |
dc.subject |
Oblique projections |
dc.subject |
Angles between subspaces |
dc.subject |
Compatibility |
dc.subject |
Abstract splines |
dc.title |
Redundant decompositions, angles between subspaces and oblique projections |
dc.type |
Article |
dc.description.abstract |
Let Η be a complex Hilbert space. We study the relationships between the angles between closed subspaces of H, the oblique projections associated to non direct decompositions of H and a notion of compatibility between a positive (semidefinite) operator A acting on H and a closed subspace S of H. It turns out that the compatibility is ruled by the values of the Dixmier angle between the orthogonal complement S _l_ of S and the closure of AS. We show that every redundant decomposition H = S+M_l_ (where redundant means that S ∩M_l_ is not trivial) occurs in the presence of a certain compatibility. We also show applications of these results to some signal processing problems (consistent reconstruction) and to abstract splines problems which come from approximation theory. |