A SIMPLE NATURAL APPROACH TO THE UNIFORM BOUNDEDNESS PRINCIPLE FOR MUTILINEAR MAPPINGS

The goal of this note is to give a new, simple and elegant proof to the Uniform Boundedness Principle (UBP) to m-linear mappings, which surprisingly, as far as we know, does not appear in the literature. The multilinear UBP is well-known for specialists but the original proof (presented in [4]) seem...

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Autor principal:	Thiago Bernandino,A
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2009
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172009000300001
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spelling	oai:scielo:S0716-091720090003000012010-04-08A SIMPLE NATURAL APPROACH TO THE UNIFORM BOUNDEDNESS PRINCIPLE FOR MUTILINEAR MAPPINGSThiago Bernandino,AThe goal of this note is to give a new, simple and elegant proof to the Uniform Boundedness Principle (UBP) to m-linear mappings, which surprisingly, as far as we know, does not appear in the literature. The multilinear UBP is well-known for specialists but the original proof (presented in [4]) seems a little bit unnatural and uses the linear UBP. In the present note we show a quite simple argument which does not need to invoke the linear UBP and, when m = 1, recovers the classical proof of the linear case. As an immediate consequence, we obtain the Banach-Steinhaus Theorem (BST) for multilinear mappings.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.28 n.3 20092009-12-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172009000300001en10.4067/S0716-09172009000300001
institution	Scielo Chile
collection	Scielo Chile
language	English
description	The goal of this note is to give a new, simple and elegant proof to the Uniform Boundedness Principle (UBP) to m-linear mappings, which surprisingly, as far as we know, does not appear in the literature. The multilinear UBP is well-known for specialists but the original proof (presented in [4]) seems a little bit unnatural and uses the linear UBP. In the present note we show a quite simple argument which does not need to invoke the linear UBP and, when m = 1, recovers the classical proof of the linear case. As an immediate consequence, we obtain the Banach-Steinhaus Theorem (BST) for multilinear mappings.
author	Thiago Bernandino,A
spellingShingle	Thiago Bernandino,A A SIMPLE NATURAL APPROACH TO THE UNIFORM BOUNDEDNESS PRINCIPLE FOR MUTILINEAR MAPPINGS
author_facet	Thiago Bernandino,A
author_sort	Thiago Bernandino,A
title	A SIMPLE NATURAL APPROACH TO THE UNIFORM BOUNDEDNESS PRINCIPLE FOR MUTILINEAR MAPPINGS
title_short	A SIMPLE NATURAL APPROACH TO THE UNIFORM BOUNDEDNESS PRINCIPLE FOR MUTILINEAR MAPPINGS
title_full	A SIMPLE NATURAL APPROACH TO THE UNIFORM BOUNDEDNESS PRINCIPLE FOR MUTILINEAR MAPPINGS
title_fullStr	A SIMPLE NATURAL APPROACH TO THE UNIFORM BOUNDEDNESS PRINCIPLE FOR MUTILINEAR MAPPINGS
title_full_unstemmed	A SIMPLE NATURAL APPROACH TO THE UNIFORM BOUNDEDNESS PRINCIPLE FOR MUTILINEAR MAPPINGS
title_sort	simple natural approach to the uniform boundedness principle for mutilinear mappings
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2009
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172009000300001
work_keys_str_mv	AT thiagobernandinoa asimplenaturalapproachtotheuniformboundednessprincipleformutilinearmappings AT thiagobernandinoa simplenaturalapproachtotheuniformboundednessprincipleformutilinearmappings
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A SIMPLE NATURAL APPROACH TO THE UNIFORM BOUNDEDNESS PRINCIPLE FOR MUTILINEAR MAPPINGS

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