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===Uniform boundedness principle===
{{main|Banach-Steinhaus theorem}}
The [[uniform boundedness principle]] or [[Banach–Steinhaus theorem]] is one of the fundamental results in functional analysis. Together with the [[Hahn–Banach theorem]] and the [[open mapping theorem (functional analysis)|open mapping theorem]], it is considered one of the cornerstones of the field. In its basic form, it asserts that for a family of [[continuous linear operator]]s (and thus bounded operators) whose ___domain is a [[Banach space]], pointwise boundedness is equivalent to uniform boundedness in operator norm.{{cn}}
The theorem was first published in 1927 by [[Stefan Banach]] and [[Hugo Steinhaus]] but it was also proven independently by [[Hans Hahn (mathematician)|Hans Hahn]].
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