| Title:
|
A note on Lipschitz isomorphisms in Hilbert spaces (English) |
| Author:
|
Ives, Dean |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
51 |
| Issue:
|
3 |
| Year:
|
2010 |
| Pages:
|
427-430 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We show that the following well-known open problems on existence of Lipschitz isomorphisms between subsets of Hilbert spaces are equivalent: Are balls isomorphic to spheres? Is the whole space isomorphic to the half space? (English) |
| Keyword:
|
Lipschitz isomorphism |
| Keyword:
|
Hilbert space |
| MSC:
|
46B03 |
| idZBL:
|
Zbl 1224.46040 |
| idMR:
|
MR2741875 |
| . |
| Date available:
|
2010-09-02T14:14:17Z |
| Last updated:
|
2013-09-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140718 |
| . |
| Reference:
|
[1] Benyamini Y., Lindenstrauss J.: Geometric Nonlinear Functional Analysis.Amer. Math. Soc. Colloquium Publications, 48, American Mathematical Society, Providence, RI, 2000. Zbl 0946.46002, MR 1727673 |
| Reference:
|
[2] Bessaga C., Pelczynski A.: Selected Topics in Infinite Dimensional Topology.PWN, Warsaw, 1975. Zbl 0304.57001, MR 0478168 |
| Reference:
|
[3] Keller O.H.: Die Homeomorphie der kompakten konvexen Mengen in Hilbertschen Raum.Math. Ann. 105 (1931), 748–758. MR 1512740, 10.1007/BF01455844 |
| Reference:
|
[4] Klee V.L.: Convex Bodies and Periodic Homeomorphisms in Hilbert Space.Trans. Amer. Math. Soc. 74 (1953), no. 1, 10–43. Zbl 0050.33202, MR 0054850, 10.1090/S0002-9947-1953-0054850-X |
| Reference:
|
[5] Nahum R.: On the Lipschitz equivalence of unit balls and spheres in normed spaces.preprint. |
| . |
