@article{Bernandino_1, title={A simple natural approach to the uniform boundedness principle for mutilinear mappings}, volume={28}, url={https://www.revistaproyecciones.cl/index.php/proyecciones/article/view/1362}, DOI={10.4067/S0716-09172009000300001}, abstractNote={<span>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.</span>}, number={3}, journal={Proyecciones (Antofagasta, On line)}, author={Bernandino, A. Thiago}, year={1}, month={1}, pages={203-207} }