On the Scottish Book Problem 155 by Mazur and Sternbach
Problem 155 of the Scottish Book asks whether every bijection $U\colon X\rightarrow Y$ between two Banach spaces $X, Y$ with the property that, each point of $X$ has a neighborhood on which $U$ is isometric, is globally isometric on $X$. We prove that this is true under the additional assumption tha...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Académie des sciences
2024-10-01
|
| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.572/ |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1825206177837875200 |
|---|---|
| author | Mori, Michiya |
| author_facet | Mori, Michiya |
| author_sort | Mori, Michiya |
| collection | DOAJ |
| description | Problem 155 of the Scottish Book asks whether every bijection $U\colon X\rightarrow Y$ between two Banach spaces $X, Y$ with the property that, each point of $X$ has a neighborhood on which $U$ is isometric, is globally isometric on $X$. We prove that this is true under the additional assumption that $X$ is separable and the weaker assumption of surjectivity instead of bijectivity. |
| format | Article |
| id | doaj-art-aed774f4f3df45d29eb95cd96bff2515 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2024-10-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-aed774f4f3df45d29eb95cd96bff25152025-02-07T11:22:49ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692024-10-01362G881381610.5802/crmath.57210.5802/crmath.572On the Scottish Book Problem 155 by Mazur and SternbachMori, Michiya0Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153-8914, Japan; Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS), RIKEN, 2-1 Hirosawa, Wako, Saitama, 351-0198, JapanProblem 155 of the Scottish Book asks whether every bijection $U\colon X\rightarrow Y$ between two Banach spaces $X, Y$ with the property that, each point of $X$ has a neighborhood on which $U$ is isometric, is globally isometric on $X$. We prove that this is true under the additional assumption that $X$ is separable and the weaker assumption of surjectivity instead of bijectivity.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.572/ |
| spellingShingle | Mori, Michiya On the Scottish Book Problem 155 by Mazur and Sternbach Comptes Rendus. Mathématique |
| title | On the Scottish Book Problem 155 by Mazur and Sternbach |
| title_full | On the Scottish Book Problem 155 by Mazur and Sternbach |
| title_fullStr | On the Scottish Book Problem 155 by Mazur and Sternbach |
| title_full_unstemmed | On the Scottish Book Problem 155 by Mazur and Sternbach |
| title_short | On the Scottish Book Problem 155 by Mazur and Sternbach |
| title_sort | on the scottish book problem 155 by mazur and sternbach |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.572/ |
| work_keys_str_mv | AT morimichiya onthescottishbookproblem155bymazurandsternbach |