Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4635852 | Applied Mathematics and Computation | 2007 | 11 Pages |
Abstract
The famous van der Waerden theorem [B.L. van der Waerden, Stetigkeitssätze für halbeinfache Liesche Gruppen, Math. Z. 36 (1933) 780-786] concerns the continuity of finite-dimensional representations of compact semisimple Lie groups. It turns out that this theorem is stable, i.e., if G is a compact semisimple Lie group and Ï : G â U(N) is a mapping for which the norm â¥Ï(ggâ²) â Ï(g)Ï(gâ²)â¥, g, gâ²Â â G, is uniformly small enough, then the mapping Ï is a small perturbation of a (necessarily continuous) ordinary unitary representation of G into U(N). This completely answers the question attributed to Milman by Kazhdan [D. Kazhdan, On ε-representations, Israel J. Math. 43 (4) (1982) 315-323] and gives a partial answer to Gromov's question [M. Gromov, Positive curvature, macroscopic dimension, spectral gaps and higher signatures, Functional Analysis on the Eve of the 21st Century, vol. II, Dordrecht, Boston, MA, 1996, pp. 1-213].
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
A.I. Shtern,