Redundant decompositions, angles between subspaces and oblique projections

 

Autores
Corach, Gustavo; Maestripieri, Alejandra Laura
Tipo de recurso
artículo
Estado
Versión publicada
Año de publicación
2010
País
Argentina
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio
CONICET Digital (CONICET)
Descripción
Let H 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⊥ of S and the closure of AS. We show that every redundant decomposition H = S+M⊥ (where redundant means that S ∩M⊥ 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.
Idioma
inglés
OAI Identifier
oai:ri.conicet.gov.ar:11336/19424
Enlace del recurso
http://hdl.handle.net/11336/19424
Nivel de acceso
Acceso abierto
Materia
OBLIQUE PROJECTIONS
ANGLE BETWEEN SUBSPACES
Matemática Pura
Matemáticas
CIENCIAS NATURALES Y EXACTAS