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Abstract:

Fusion frames, and, more generally, operator-valued frame sequences are generalizations of classical frames, which are today a standard notion when redundant, yet stable sequences are required. However, the question of stability of duals with respect to perturbations has not been satisfactorily answered. In this paper, we quantitatively measure this stability by considering the associated deviations of the canonical and alternate dual sequences from the original ones. It is proven that operator-valued frame sequences are indeed stable in this sense. Along the way, we also generalize existing definitions for fusion frame duals to the infinite-dimensional situation and analyze how they perform with respect to a list of desiderata which, to our minds, a fusion frame dual should satisfy. Finally, we prove a similar stability result as above for fusion frames and their canonical duals. © ELEMEN, Zagreb.

Registro:

Documento: Artículo
Título:The effect of perturbations of operator-valued frame sequences and fusion frames on their duals
Autor:Kutyniok, G.; Paternostro, V.; Philipp, F.
Filiación:Institut für Mathematik, Technische Universität Berlin, Straße des 17. Juni 136, Berlin, 10623, Germany
Universidad de Buenos Aires and IMAS-CONICET, Ciudad Universitaria Pabellón I, Buenos Aires, 1428, Argentina
Universidad de Buenos Aires, Ciudad Universitaria Pabellón I, Buenos Aires, 1428, Argentina
Palabras clave:Dual frame; Frame sequence; Fusion frame; Fusion frame dual; Operator-valued frame; Perturbation
Año:2017
Volumen:11
Número:2
Página de inicio:301
Página de fin:336
DOI: http://dx.doi.org/10.7153/oam-11-20
Título revista:Operators and Matrices
Título revista abreviado:Oper. Matrices
ISSN:18463886
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_18463886_v11_n2_p301_Kutyniok

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Citas:

---------- APA ----------
Kutyniok, G., Paternostro, V. & Philipp, F. (2017) . The effect of perturbations of operator-valued frame sequences and fusion frames on their duals. Operators and Matrices, 11(2), 301-336.
http://dx.doi.org/10.7153/oam-11-20
---------- CHICAGO ----------
Kutyniok, G., Paternostro, V., Philipp, F. "The effect of perturbations of operator-valued frame sequences and fusion frames on their duals" . Operators and Matrices 11, no. 2 (2017) : 301-336.
http://dx.doi.org/10.7153/oam-11-20
---------- MLA ----------
Kutyniok, G., Paternostro, V., Philipp, F. "The effect of perturbations of operator-valued frame sequences and fusion frames on their duals" . Operators and Matrices, vol. 11, no. 2, 2017, pp. 301-336.
http://dx.doi.org/10.7153/oam-11-20
---------- VANCOUVER ----------
Kutyniok, G., Paternostro, V., Philipp, F. The effect of perturbations of operator-valued frame sequences and fusion frames on their duals. Oper. Matrices. 2017;11(2):301-336.
http://dx.doi.org/10.7153/oam-11-20