Three old problems from the Polish school of mathematics-Reference-Cited by-同舟云学术

Three old problems from the Polish school of mathematics

Published:2024-07 Issue:2 Volume:30 Page:
ISSN:1405-213X
Container-title:Boletín de la Sociedad Matemática Mexicana
language:en
Short-container-title:Bol. Soc. Mat. Mex.

Author:

Montejano Luis^ORCID

Abstract

AbstractThis note deals with three problems posed in the 1930s by two prominent members of the Polish school of mathematics. The first problem is known as the isometric Banach conjecture and deals with the simplest characterization of Hilbert spaces among Banach spaces. It was stated in 1932 by Stephan Banach in his book Théorie des opérations linéaires, 1987. The second is Problem 68 in the Scottish Book, 2015, posed by Stanislaw Ulam in 1936, and the third is the well known floating body problem stated by Stanislaw Ulam in 1935 and which is also known as Problem 19 of the Scottish Book.

Funder

Universidad Nacional Autónoma de México

Publisher

Springer Science and Business Media LLC

Link

https://link.springer.com/content/pdf/10.1007/s40590-024-00637-0.pdf

Reference31 articles.

1. Auerbach, H.: Sur un probleme concernant l’equilibre des corps flottant. Studia Math. 7, 121–142 (1938)

2. Auerbach, H., Mazur, S., Ulam, S.: Sur une propriété caractéristique de l’ellipsoïde. Monastshe. Math. Phys. 42, 45–48 (1935)

3. Aumann, G.: Eine einfache Characterisierung der convexen Kontinuen in $$R^{3}$$. Deutsche Mathematik 1, 108 (1936)

4. Banach, S.: Théorie des opérations linéaires, Monografie Matematyczne, 1932. English translation: Theory of Linear Operations. Vol. 38. Elsevier, (1987)

5. Bor, G., Hernández-Lamoneda, L., Jiménez-Desantiago, V., Montejano, L.: On the isometric conjecture of Banach. Geom. Topol. 25(5), 2621–2642 (2021)