Decomposable symmetric mappings between infinite-dimensional spaces

Mostrar todas las versiones(3)

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...

Descripción completa

Guardado en:
Detalles Bibliográficos
Autores principales: Boyd, C., Lassalle, S.
Formato: Artículo publishedVersion
Publicado: 2008
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00042080_v46_n1_p7_Boyd
https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00042080_v46_n1_p7_Boyd_oai
Aporte de:
Repositorio Digital de la Universidad de Buenos Aires (UBA) de Universidad de Buenos Aires
id I28-R145-paper_00042080_v46_n1_p7_Boyd_oai
record_format dspace
spelling I28-R145-paper_00042080_v46_n1_p7_Boyd_oai2024-08-16 Boyd, C. Lassalle, S. 2008 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. application/pdf http://hdl.handle.net/20.500.12110/paper_00042080_v46_n1_p7_Boyd info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar Ark. Mat. 2008;46(1):7-29 Decomposable symmetric mappings between infinite-dimensional spaces info:eu-repo/semantics/article info:ar-repo/semantics/artículo info:eu-repo/semantics/publishedVersion https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00042080_v46_n1_p7_Boyd_oai
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-145
collection Repositorio Digital de la Universidad de Buenos Aires (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 Artículo
Artículo
publishedVersion
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
publishDate 2008
url http://hdl.handle.net/20.500.12110/paper_00042080_v46_n1_p7_Boyd
https://repositoriouba.sisbi.uba.ar/gsdl/cgi-bin/library.cgi?a=d&c=artiaex&d=paper_00042080_v46_n1_p7_Boyd_oai
work_keys_str_mv AT boydc decomposablesymmetricmappingsbetweeninfinitedimensionalspaces
AT lassalles decomposablesymmetricmappingsbetweeninfinitedimensionalspaces
_version_ 1809356759463100416

Ejemplares similares