DOI: http://dx.doi.org/10.18273/revint.v34n1-2016005
Construction and coupling of frames in
Hilbert spaces with W-metrics
GERMAN ESCOBARa, KEVIN ESMERALb, OSMIN FERRERb*
a Universidad Surcolombiana, Programa de Matemática Aplicada, Neiva, Colombia.
b Universidad de Sucre, Departamento de Matemáticas, Sincelejo, Colombia.
Dedicated to the memory of our dear friend
Ricardo Cedeño
Abstract. A definition of frames unitarily equivalent in Hilbert spaces with W-metric is stated, and a characterization is given in terms of their respective analysis operators. From a Hilbert space with a frame we construct a Hilbert space with W-metric and a frame unitarily equivalent to the given one. Finally, we prove that the coupling of two frames is a frame.
]]> Keywords: Krein spaces, W-spaces, W-metrics, construction of frames, coupling of frames, similar frames.Construcción y acoplamiento de marcos en
espacios de Hilbert con W-métricas
Resumen. Se definen marcos unitariamente equivalentes en espacios de Hilbert con W-métricas, y se da una caracterización de ellos comparando sus respectivos operadores de análisis. A partir de un espacio de Hilbert con un marco se construye un espacio de Hilbert con W-métrica y un marco unitariamente equivalente al dado. Finalmente, se muestra que el acoplamiento de dos marcos es un marco.
Palabras clave: Espacios de Krein, W-espacios, W-métricas, construcción de marcos, acoplamiento de marcos, marcos similares.
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