Banach Journal of Mathematical Analysis

On Stefan Banach and some of his results

Krzysztof Ciesielski

Full-text: Open access


Banach Journal of Mathematical Analysis is named after one of the most outstanding mathematicians in the XXth century, Stefan Banach. Thus it is natural to recall in the first issue of the journal some information about Banach. A very short biography, some of his most eminent results and some stories will be presented in this article.

Article information

Banach J. Math. Anal., Volume 1, Number 1 (2007), 1-10.

First available in Project Euclid: 21 April 2009

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 01A60: 20th century
Secondary: 46-03: Historical (must also be assigned at least one classification number from Section 01) 46B25: Classical Banach spaces in the general theory

Banach functional analysis Scottish Cafe Lvov School of mathematics Banach space


Ciesielski , Krzysztof. On Stefan Banach and some of his results. Banach J. Math. Anal. 1 (2007), no. 1, 1--10. doi:10.15352/bjma/1240321550.

Export citation


  • L. Alaoglu, Weak topologies of normed linear spaces, Ann. Math. 41 (1940), 252–267.
  • S. Banach, Sur le probléme de la mesure, Fund. Math. 4 (1924), 7–33.
  • S. Banach, Sur les fonctionelles linéaires, Studia Math. 1 (1929), 211–216.
  • S. Banach, Sur les fonctionelles linéaires II, Studia Math. 1 (1929), 223–239.
  • S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math. 3 (1922), 133–181.
  • S. Banach, Théorie des opérations linéaires, Monografie Matematyczne 1, Warszawa 1932.
  • S. Banach, H.Steinhaus, Sur le principle de la condensation de singularités, Fund. Math. 9 (1927), 50–61.
  • H.F. Bohnenblust and A.Sobczyk, Extensions of fuctionals on complete linear spaces, Bull. Amer. Math. Soc. Fund. Math. 44 (1938), 91–93.
  • S. Banach and A. Tarski, Sur la décomposition des ensembles de points en parties respectivement congruentes, Fund. Math. 6 (1924), 244–277.
  • K. Ciesielski, Lost Legends of Lvov 1: The Scottish Café, Math. Intelligencer 9 (1987) no.4, 36–37.
  • K. Ciesielski, Lost Legends of Lvov 2: Banach's Grave, Math. Intelligencer 10 (1988) no.1, 50–51.
  • K. Ciesielski, On some details of Stefan Banach's life, Opuscula Math. 13 (1993), 71–74.
  • K. Ciesielski and Z.Pogoda, Conversation with Andrzej Turowicz, Math. Intelligencer 10 (1988) no.4, 13–20.
  • K. Ciesielski and Z.Pogoda, Mathematical diamonds, manuscript, the translation from the book published in Polish “Diamenty matematyki", Prószyński i S-ka, 1997.
  • R. Duda, The discovery of Banach spaces, in: European mathematics in the last centuries (W. Więsław, ed.), Wrocław 2005, 37–46.
  • N. Dunford and J.T. Schwartz, Linear Operators, Interscience Publishers, New York, vol. I, 1958.
  • P. Enflo, A counterexample to the approximation property in Banach spaces, Acta Math. 130 (1973), 309–317.
  • R.M. French, The Banach-Tarski theorem, Math. Intelligencer 10 (1988) no.4, 21–28.
  • A. Grothendieck, Produits tensoriels topologiques et espaces nucleaires, Mem. Amer. Math. Soc. 16 (1955).
  • H. Hahn, Über lineare Gleichungssysteme in linearen Räumen, J. Reine Angew. Math. 157 (1927) 214–229.
  • E. Helly, Über lineare operationenen, Sitzgsber. Akad. Wiss. Wien. Math-Nat. 121 (1912), 265–297.
  • H. Hochstadt and E. Helly, Father of the Hahn-Banach Theorem, Math. Intelligencer 2 (1980), no. 3, 123–125.
  • D. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. USA 121 (1941), 222-224.
  • D.H. Hyers and T.M. Rassias, Approximate homomorphisms, Aequationes Math., 44 (1992), 125–153.
  • E. Jakimowicz and A. Miranowicz (eds.), Stefan Banach – remarkable life, brilliant mathematics, Gdańsk University Press, Adam Mickiewicz University Press, 2007.
  • R. Kałuża, Through a reporter's eyes. The Life of Stefan Banach, Birkhäuser 1996.
  • R.D. Mauldin (ed.), The Scottish Book. Mathematics from the Scottish Café, Birkhäuser, 1981.
  • T.M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72 (1978), 297–300.
  • W. Rudin, Functional analysis, second edition, McGraw-Hill, 1991.
  • M.Reed, B.Simon, Methods of modern mathematical physics, I. Functional analysis, Academic Press, 1972.
  • G.A. Soukhomlinov, Über Fortsetzung von linearen Funktionalen in linearen komplexen Räumen und linearen Quaternionenräumen, Mat. Sb., 3 (1938), 353–358.
  • S. Ulam 1909–1984. Los Alamos Sci. No. 15, Special Issue (1987), Los Alamos National Laboratory, Los Alamos, NM, 1987. pp., 1–318.