A really simple elementary proof of the uniform boundedness principle in F-spaces
Abstract
We give a proof of the uniform boundedness principle for linear continuous maps from F-spaces into topological vector spaces which is elementary and also quite simple.
Keywords
uniform boundedness; Baire category; metric linear space; topological vector space
References
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N.J. Kalton, N.T. Peck, and J.W. Roberts, An F-space Sampler, London Math. Soc. Lecture Note Ser., 89, Cambridge University Press, Cambridge, 1984.
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A.D. Sokal, A really simple elementary proof of the uniform boundedness theorem, Amer. Math. Monthly 118 (2011), no. 5, 450–452.
C. Swartz, The evolution of the uniform boundedness principle, Math. Chronicle 19 (1990), 1–18.
Department of Mathematics and Computer Sciences, Universidad de La Rioja Spain
https://orcid.org/0000-0002-4979-1080
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