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Articles

From Uniform Boundedness to the Boundary Between Convergence and Divergence

Pages 525-531 | Received 10 Jan 2020, Accepted 13 May 2020, Published online: 19 Oct 2022

References

  • Abel, N. H. (1828). Note sur le mémoire de Mr. L. Olivier No. 4. du second tome de ce journal, ayant pour titre “Remarques sur les séries infinies et leur convergence”. Journal für die Reine und Angewandte Mathematik, 3(1): 79–82.
  • Ash, J. M. (1997). Neither a worst convergent series nor a best divergent series exists. Coll. Math. J. 28(4): 296–297. DOI: 10.1080/07468342.1997.11973879.
  • Carothers, N. L. (2005). A Short Course on Banach Space Theory. Cambridge: Cambridge Univ. Press.
  • Dini, U. (1867). Sulle serie a termini positivi. Ann. Univ. Toscana. 9:41–76.
  • Du Bois-Reymond, P. (1873). Eine neue Theorie der Convergenz und Divergenz von Reihen mit positiven Gliedern. Journal für die reine und angewandte Mathematik, 76: 61–91. DOI: 10.1515/crll.1873.76.61.
  • Gowers, T., Barrow-Green, J., Leader, I., eds. (2008). The Princeton Companion to Mathematics. Princeton: Princeton Univ. Press.
  • Kałuża, R. (1996). The Life of Stefan Banach. Boston: Birkhäuser.
  • Knopp, K. (1928). Theory and Application of Infinite Series. Glasgow: Blackie & Son.
  • Riesz, F., Sz.-Nagy, B. (1990). Functional Analysis. New York: Dover.
  • Sokal, A. D. (2011). A really simple elementary proof of the uniform boundedness theorem. Amer. Math. Monthly. 118(5): 450–452. DOI: 10.4619/amer.math.monthly.118.05.450.
  • Tao, T. (2010). An epsilon of room, I: Real analysis, vol. 117 of Graduate Studies in Mathematics. Providence, RI: American Mathematical Society.

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