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Abstract:

Decomposable mappings from the space of symmetric k-fold tensors over E, O×s,kE, to the space of k-fold tensors over F, O×s,kF, are those linear operators which map nonzero decomposable elements to nonzero decomposable elements. We prove that any decomposable mapping is induced by an injective linear operator between the spaces on which the tensors are defined. Moreover, if the decomposable mapping belongs to a given operator ideal, then so does its inducing operator. This result allows us to classify injective linear operators between spaces of homogeneous approximable polynomials and between spaces of nuclear polynomials which map rank-1 polynomials to rank-1 polynomials. © 2007 Institut Mittag-Leffler.

Registro:

Documento: Artículo
Título:Decomposable symmetric mappings between infinite-dimensional spaces
Autor:Boyd, C.; Lassalle, S.
Filiación:School of Mathematical Sciences, University College Dublin, Belfield, Dublin 4, Ireland
Departamento de Matemática, Pab. i - Ciudad Universitaria (FCEN), Universidad de Buenos Aires, Buenos Aires 1428, Argentina
Año:2008
Volumen:46
Número:1
Página de inicio:7
Página de fin:29
DOI: http://dx.doi.org/10.1007/s11512-007-0061-x
Título revista:Arkiv for Matematik
Título revista abreviado:Ark. Mat.
ISSN:00042080
PDF:https://bibliotecadigital.exactas.uba.ar/download/paper/paper_00042080_v46_n1_p7_Boyd.pdf
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00042080_v46_n1_p7_Boyd

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Citas:

---------- APA ----------
Boyd, C. & Lassalle, S. (2008) . Decomposable symmetric mappings between infinite-dimensional spaces. Arkiv for Matematik, 46(1), 7-29.
http://dx.doi.org/10.1007/s11512-007-0061-x
---------- CHICAGO ----------
Boyd, C., Lassalle, S. "Decomposable symmetric mappings between infinite-dimensional spaces" . Arkiv for Matematik 46, no. 1 (2008) : 7-29.
http://dx.doi.org/10.1007/s11512-007-0061-x
---------- MLA ----------
Boyd, C., Lassalle, S. "Decomposable symmetric mappings between infinite-dimensional spaces" . Arkiv for Matematik, vol. 46, no. 1, 2008, pp. 7-29.
http://dx.doi.org/10.1007/s11512-007-0061-x
---------- VANCOUVER ----------
Boyd, C., Lassalle, S. Decomposable symmetric mappings between infinite-dimensional spaces. Ark. Mat. 2008;46(1):7-29.
http://dx.doi.org/10.1007/s11512-007-0061-x