Group Riesz and frame sequences: the Bracket and the Gramian

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 fr...

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Detalles Bibliográficos
Autores principales:	Barbieri, D., Hernández, E., Paternostro, V.
Formato:	JOUR
Materias:	Bracket map Gramian operator Group von Neumann algebras Invariant subspaces Riesz and frame sequences
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_00100757_v69_n2_p221_Barbieri
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	todo:paper_00100757_v69_n2_p221_Barbieri
record_format	dspace
spelling	todo:paper_00100757_v69_n2_p221_Barbieri2023-10-03T14:08:59Z Group Riesz and frame sequences: the Bracket and the Gramian Barbieri, D. Hernández, E. Paternostro, V. Bracket map Gramian operator Group von Neumann algebras Invariant subspaces Riesz and frame sequences 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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00100757_v69_n2_p221_Barbieri
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	Bracket map Gramian operator Group von Neumann algebras Invariant subspaces Riesz and frame sequences
spellingShingle	Bracket map Gramian operator Group von Neumann algebras Invariant subspaces Riesz and frame sequences Barbieri, D. Hernández, E. Paternostro, V. Group Riesz and frame sequences: the Bracket and the Gramian
topic_facet	Bracket map Gramian operator Group von Neumann algebras Invariant subspaces Riesz and frame sequences
description	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.
format	JOUR
author	Barbieri, D. Hernández, E. Paternostro, V.
author_facet	Barbieri, D. Hernández, E. Paternostro, V.
author_sort	Barbieri, D.
title	Group Riesz and frame sequences: the Bracket and the Gramian
title_short	Group Riesz and frame sequences: the Bracket and the Gramian
title_full	Group Riesz and frame sequences: the Bracket and the Gramian
title_fullStr	Group Riesz and frame sequences: the Bracket and the Gramian
title_full_unstemmed	Group Riesz and frame sequences: the Bracket and the Gramian
title_sort	group riesz and frame sequences: the bracket and the gramian
url	http://hdl.handle.net/20.500.12110/paper_00100757_v69_n2_p221_Barbieri
work_keys_str_mv	AT barbierid grouprieszandframesequencesthebracketandthegramian AT hernandeze grouprieszandframesequencesthebracketandthegramian AT paternostrov grouprieszandframesequencesthebracketandthegramian
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Group Riesz and frame sequences: the Bracket and the Gramian

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