A Really Simple Elementary Proof of the Uniform Boundedness Theorem

2010/05/31 by Alan D. Sokal · 1 citation
Computer Science · Mathematics · #Advanced Banach Space Theory #Advanced Operator Algebra Research #Baire category theorem #Brouwer fixed-point theorem #Elementary proof #Logic, programming, and type systems #Simple (philosophy) #Uniform boundedness #Uniform continuity #Uniform convergence #Uniform limit theorem #math.FA #msc:46B20 #msc:46B28 #msc:46B99

paper · pdf · doi:10.4169/amer.math.monthly.118.05.450

published as Amer. Math. Monthly 118, 450-452 (2011) · LaTex2e, 5 pages. Version 2 improves the exposition by isolating the key lemma. To appear in the American Mathematical Monthly

arxiv created 2010/12/29 · openalex publication_date 2011/05/01 · arxiv updated 2011/05/03 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

I give a proof of the uniform boundedness theorem that is elementary (i.e., does not use any version of the Baire category theorem) and also extremely simple.

Citations

• Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales
• The plank problem for symmetric bodies
• Sur le principe de la condensation de singularités

Cited by

• Uniform boundedness principle [wikipedia]