Construction and coupling of frames in Hilbert spaces with W … · 2016. 10. 27. · Hilbert space...
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∮Revista Integración
Escuela de Matemáticas
Universidad Industrial de Santander
Vol. 34, No. 1, 2016, pág. 81–93
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 withW-metric is stated, and a characterization is given in terms of their respec-tive analysis operators. From a Hilbert space with a frame we construct aHilbert space with W-metric and a frame unitarily equivalent to the givenone. Finally, we prove that the coupling of two frames is a frame.Keywords: Krein spaces, W-spaces, W-metrics, construction of frames, cou-pling 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 deHilbert con W-métricas, y se da una caracterización de ellos comparandosus respectivos operadores de análisis. A partir de un espacio de Hilbertcon un marco se construye un espacio de Hilbert con W-métrica y unmarco unitariamente equivalente al dado. Finalmente, se muestra que elacoplamiento de dos marcos es un marco.Palabras clave: Espacios de Krein, W-espacios, W-métricas, construcción demarcos, acoplamiento de marcos, marcos similares.
0∗E-mail: [email protected]
Received: 18 August 2015, Accepted: 08 March 2016.To cite this article: G. Escobar, K. Esmeral, O. Ferrer, Construction and coupling of frames in Hilbertspaces with W-metrics, Rev. Integr. Temas Mat. 34 (2016), No. 1, 81–93.
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DOI: http://dx.doi.org/10.18273/revint.v34n1-2016005
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