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| Pàgina inicial > Articles > Articles publicats > Redundant decompositions, angles between subspaces and oblique projections |
| Data: | 2010 |
| Resum: | 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. |
| Drets: | Tots els drets reservats.  |
| Llengua: | Anglès |
| Document: | Article ; recerca ; Versió publicada |
| Matèria: | Oblique projections ; Angles between subspaces ; Compatibility ; Abstract splines |
| Publicat a: | Publicacions matemàtiques, Vol. 54, Núm. 2 (2010) , p. 461-484, ISSN 2014-4350 |
