Decomposable symmetric mappings between infinite-dimensional spaces

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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 linea...

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Autores principales: Boyd, C., Lassalle, S.
Formato: JOUR
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00042080_v46_n1_p7_Boyd
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_00042080_v46_n1_p7_Boyd
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spelling todo:paper_00042080_v46_n1_p7_Boyd2023-10-03T13:57:12Z Decomposable symmetric mappings between infinite-dimensional spaces Boyd, C. Lassalle, S. 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. Fil:Lassalle, S. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00042080_v46_n1_p7_Boyd
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
description 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.
format JOUR
author Boyd, C.
Lassalle, S.
spellingShingle Boyd, C.
Lassalle, S.
Decomposable symmetric mappings between infinite-dimensional spaces
author_facet Boyd, C.
Lassalle, S.
author_sort Boyd, C.
title Decomposable symmetric mappings between infinite-dimensional spaces
title_short Decomposable symmetric mappings between infinite-dimensional spaces
title_full Decomposable symmetric mappings between infinite-dimensional spaces
title_fullStr Decomposable symmetric mappings between infinite-dimensional spaces
title_full_unstemmed Decomposable symmetric mappings between infinite-dimensional spaces
title_sort decomposable symmetric mappings between infinite-dimensional spaces
url http://hdl.handle.net/20.500.12110/paper_00042080_v46_n1_p7_Boyd
work_keys_str_mv AT boydc decomposablesymmetricmappingsbetweeninfinitedimensionalspaces
AT lassalles decomposablesymmetricmappingsbetweeninfinitedimensionalspaces
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