Artículo
Parametrizing projections with selfadjoint operators
Fecha de publicación:
01/2015
Editorial:
Elsevier Science Inc
Revista:
Linear Algebra And Its Applications
ISSN:
0024-3795
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
Let H=H+⊕H− be an orthogonal decomposition of a Hilbert space, with E+, E− the corresponding projections. Let A be a selfadjoint operator in H which is codiagonal with respect to this decomposition (i.e. A(H+)⊂H− and A(H−)⊂H+). We consider three maps which assign a selfadjoint projection to A: 1.The graph map Γ : Γ(A)=projection onto the graph of A|H+. 2.The exponential map of the Grassmann manifold P of H (the space of selfadjoint projections in H) at E+: . 3.The map p, called here the Davis' map, based on a result by Chandler Davis, characterizing the selfadjoint contractions which are the difference of two projections. The ranges of these maps are studied and compared. Using Davis' map, one can solve the following operator matrix completion problem: given a contraction a:H−→H+, complete the matrix to a projection P , in order that ‖P−E+‖ is minimal.
Palabras clave:
Projection
,
Selfadjoint Operator
Archivos asociados
Licencia
Identificadores
Colecciones
Articulos(IAM)
Articulos de INST.ARG.DE MATEMATICAS "ALBERTO CALDERON"
Articulos de INST.ARG.DE MATEMATICAS "ALBERTO CALDERON"
Articulos(SEDE CENTRAL)
Articulos de SEDE CENTRAL
Articulos de SEDE CENTRAL
Citación
Andruchow, Esteban; Parametrizing projections with selfadjoint operators; Elsevier Science Inc; Linear Algebra And Its Applications; 466; 1-2015; 307-328
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