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]) 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.
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| Format: | Digital revista |
| Language: | English |
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Universidad Católica del Norte, Departamento de Matemáticas
2009
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| Online Access: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172009000300001 |
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