uniform boundedness principle
theorem that a pointwise bounded set of linear operators on a Banach space is uniformly bounded in operator norm
Press Enter · cited answer in seconds
0 sources
uniform boundedness principle
Summary
uniform boundedness principle is a theorem[1]. It draws 197 Wikipedia views per month (theorem category, ranking #157 of 1,306).[2]
Key Facts
- uniform boundedness principle's instance of is recorded as theorem[3].
- Stefan Banach is named after uniform boundedness principle[4].
- Hugo Steinhaus is named after uniform boundedness principle[5].
- uniform boundedness principle's part of is recorded as list of theorems[6].
- uniform boundedness principle's Freebase ID is recorded as /m/01ksg8[7].
- uniform boundedness principle's defining formula is recorded as \forall F\subset B(X,Y)\colon\left(\left(\forall x\in X\colon\sup_{T \in F} |T(x)|Y < \infty\right)\implies\sup{T\in F}|T|{B(X,Y)}<\infty\right)<sup id="cite-C16" class="cite-ref" title="uniform boundedness principle — defining formula (P2534): \forall F\subset B(X,Y)\colon\left(\left(\forall x\in X\colon\sup{T \in F} |T(x)|Y < \infty\right)\implies\sup{T\in F}|T|_{B(X,Y)}<\in">[8].
- uniform boundedness principle's MathWorld ID is recorded as Banach-SteinhausTheorem[9].
- uniform boundedness principle's maintained by WikiProject is recorded as WikiProject Mathematics[10].
- uniform boundedness principle's Microsoft Academic ID is recorded as 150873688[11].
- uniform boundedness principle's ProofWiki ID is recorded as Banach-Steinhaus_Theorem[12].
- uniform boundedness principle's in defining formula is recorded as X[13].
- uniform boundedness principle's in defining formula is recorded as Y[14].
- uniform boundedness principle's in defining formula is recorded as |-|_{B(X,Y)}[15].
- uniform boundedness principle's Encyclopedia of Mathematics article ID is recorded as Banach-Steinhaus_theorem[16].
- uniform boundedness principle's ScienceDirect topic ID is recorded as mathematics/banach-steinhaus-theorem[17].
Why It Matters
uniform boundedness principle draws 197 Wikipedia views per month (theorem category, ranking #157 of 1,306).[2] It has Wikipedia articles in 17 language editions, a strong signal of global cultural recognition.[18] It is known by 16 alternative names across languages and contexts.[19]