DOI: http://dx.doi.org/10.18273/revint.v34n1-2016005

Construction and coupling of frames in
Hilbert spaces with W-metrics

GERMAN ESCOBAR^a, KEVIN ESMERAL^b, OSMIN FERRER^b*

^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.
MSC2010: 42C15, 47B50, 46C20.

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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^*E-mail: osmin.ferrer@unisucre.edu.co.
Received: 18 August 2015, Accepted: 08 March 2016.
To cite this article: G. Escobar, K. Esmeral, O. Ferrer, Construction and coupling of frames in Hilbert spaces with W-metrics, Rev. Integr. Temas Mat. 34 (2016), No. 1, 81-93.