A note on Lipschitz isomorphisms in Hilbert spaces
Commentationes Mathematicae Universitatis Carolinae (2010)
- Volume: 51, Issue: 3, page 427-430
- ISSN: 0010-2628
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topIves, Dean. "A note on Lipschitz isomorphisms in Hilbert spaces." Commentationes Mathematicae Universitatis Carolinae 51.3 (2010): 427-430. <http://eudml.org/doc/38138>.
@article{Ives2010,
abstract = {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?},
author = {Ives, Dean},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Lipschitz isomorphism; Hilbert space; Lipschitz isomorphism; Hilbert space},
language = {eng},
number = {3},
pages = {427-430},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A note on Lipschitz isomorphisms in Hilbert spaces},
url = {http://eudml.org/doc/38138},
volume = {51},
year = {2010},
}
TY - JOUR
AU - Ives, Dean
TI - A note on Lipschitz isomorphisms in Hilbert spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2010
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 51
IS - 3
SP - 427
EP - 430
AB - 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?
LA - eng
KW - Lipschitz isomorphism; Hilbert space; Lipschitz isomorphism; Hilbert space
UR - http://eudml.org/doc/38138
ER -
References
top- Benyamini Y., Lindenstrauss J., Geometric Nonlinear Functional Analysis, Amer. Math. Soc. Colloquium Publications, 48, American Mathematical Society, Providence, RI, 2000. Zbl0946.46002MR1727673
- Bessaga C., Pelczynski A., Selected Topics in Infinite Dimensional Topology, PWN, Warsaw, 1975. Zbl0304.57001MR0478168
- Keller O.H., 10.1007/BF01455844, Math. Ann. 105 (1931), 748–758. MR1512740DOI10.1007/BF01455844
- Klee V.L., 10.1090/S0002-9947-1953-0054850-X, Trans. Amer. Math. Soc. 74 (1953), no. 1, 10–43. Zbl0050.33202MR0054850DOI10.1090/S0002-9947-1953-0054850-X
- Nahum R., On the Lipschitz equivalence of unit balls and spheres in normed spaces, preprint.
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