Abstract:
Given a discrete group and a unitary representation on a Hilbert space H, we prove that the notions of operator Bracket map and Gramian coincide on a dense set of H. As a consequence, combining this result with known frame theory, we can recover all previous Bracket characterizations of Riesz and frame sequences generated by a single element under a unitary representation. © 2017, Universitat de Barcelona.
Registro:
Documento: |
Artículo
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Título: | Group Riesz and frame sequences: the Bracket and the Gramian |
Autor: | Barbieri, D.; Hernández, E.; Paternostro, V. |
Filiación: | Universidad Autónoma de Madrid, Madrid, 28049, Spain Universidad de Buenos Aires and IMAS-CONICET, Consejo Nacional de Investigaciones Científicas y Técnicas, Buenos Aires, 1428, Argentina
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Palabras clave: | Bracket map; Gramian operator; Group von Neumann algebras; Invariant subspaces; Riesz and frame sequences |
Año: | 2018
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Volumen: | 69
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Número: | 2
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Página de inicio: | 221
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Página de fin: | 236
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DOI: |
http://dx.doi.org/10.1007/s13348-017-0202-x |
Título revista: | Collectanea Mathematica
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Título revista abreviado: | Collect. Math.
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ISSN: | 00100757
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00100757_v69_n2_p221_Barbieri |
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Citas:
---------- APA ----------
Barbieri, D., Hernández, E. & Paternostro, V.
(2018)
. Group Riesz and frame sequences: the Bracket and the Gramian. Collectanea Mathematica, 69(2), 221-236.
http://dx.doi.org/10.1007/s13348-017-0202-x---------- CHICAGO ----------
Barbieri, D., Hernández, E., Paternostro, V.
"Group Riesz and frame sequences: the Bracket and the Gramian"
. Collectanea Mathematica 69, no. 2
(2018) : 221-236.
http://dx.doi.org/10.1007/s13348-017-0202-x---------- MLA ----------
Barbieri, D., Hernández, E., Paternostro, V.
"Group Riesz and frame sequences: the Bracket and the Gramian"
. Collectanea Mathematica, vol. 69, no. 2, 2018, pp. 221-236.
http://dx.doi.org/10.1007/s13348-017-0202-x---------- VANCOUVER ----------
Barbieri, D., Hernández, E., Paternostro, V. Group Riesz and frame sequences: the Bracket and the Gramian. Collect. Math. 2018;69(2):221-236.
http://dx.doi.org/10.1007/s13348-017-0202-x