A Really Simple Elementary Proof of the Uniform Boundedness Principle in F-spaces

[1] S. Banach and H. Steinhaus, Sur le principe de la condensation de singularités, Fund. Math. 9 (1927), 50–60. BanachS. SteinhausH. Sur le principe de la condensation de singularités Fund. Math. 9 1927 50 60 Search in Google Scholar

[2] 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. KaltonN.J. PeckN.T. RobertsJ.W. An F-space Sampler London Math. Soc. Lecture Note Ser., 89, Cambridge University Press Cambridge 1984 Search in Google Scholar

[3] W. Rudin, Functional Analysis, Second ed., Internat. Ser. Pure Appl. Math., McGraw-Hill, Inc., New York, 1991. RudinW. Functional Analysis Second ed. Internat. Ser. Pure Appl. Math., McGraw-Hill, Inc. New York 1991 Search in Google Scholar

[4] A.D. Sokal, A really simple elementary proof of the uniform boundedness theorem, Amer. Math. Monthly 118 (2011), no. 5, 450–452. SokalA.D. A really simple elementary proof of the uniform boundedness theorem Amer. Math. Monthly 118 2011 5 450 452 Search in Google Scholar

[5] C. Swartz, The evolution of the uniform boundedness principle, Math. Chronicle 19 (1990), 1–18. SwartzC. The evolution of the uniform boundedness principle Math. Chronicle 19 1990 1 18 Search in Google Scholar