@article {MATHEDUC.05898742,
author = {Sokal, Alan D.},
title = {A really simple elementary proof of the uniform boundedness theorem.},
year = {2011},
journal = {American Mathematical Monthly},
volume = {118},
number = {5},
issn = {0002-9890},
pages = {450-452},
publisher = {Mathematical Association of America (MAA), Washington, DC},
doi = {10.4169/amer.math.monthly.118.05.450},
abstract = {The paper lives up to its title: based on the easy lemma that $\sup_{\|y-x\|0$, the author's proof constructs in just five lines some $x_0\in X$ with $\sup_n \|T_nx_0\|=\infty$ provided that $\sup_n \|T_n\|=\infty$. A wealth of information on other elementary arguments, i.e., those avoiding the Baire category theorem, complements the author's proof.},
reviewer = {Dirk Werner (Berlin)},
msc2010 = {I95xx},
identifier = {2011f.00591},
}