Redundant decompositions, angles between subspaces and oblique projections
Corach, G. (Universidad de Buenos Aires. Departamento de Matemática)
Maestripieri, Alejandra (Universidad de Buenos Aires. Departamento de Matemática)

Date:	2010
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.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Oblique projections ; Angles between subspaces ; Compatibility ; Abstract splines
Published in:	Publicacions matemàtiques, Vol. 54, Núm. 2 (2010) , p. 461-484, ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/191393
DOI: 10.5565/PUBLMAT_54210_09

24 p, 249.5 KB

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