Back to Search
Start Over
Geometric version of Wigner's theorem for Hilbert Grassmannians.
- Source :
-
Journal of Mathematical Analysis & Applications . Mar2018, Vol. 459 Issue 1, p135-144. 10p. - Publication Year :
- 2018
-
Abstract
- Let H be a complex Hilbert space of dimension not less than 3 and let G k ( H ) be the Grassmannian formed by k -dimensional subspaces of H . Suppose that dim H ≥ 2 k > 2 . We show that the transformations of G k ( H ) induced by linear or conjugate-linear isometries can be characterized as transformations preserving some of principal angles (corresponding to the orthogonality, adjacency and ortho-adjacency relations). As a consequence, we get the following: if the dimension of H is finite and greater than 2 k , then every transformation of G k ( H ) preserving the orthogonality relation in both directions is a bijection induced by a unitary or anti-unitary operator. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 0022247X
- Volume :
- 459
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of Mathematical Analysis & Applications
- Publication Type :
- Academic Journal
- Accession number :
- 126455924
- Full Text :
- https://doi.org/10.1016/j.jmaa.2017.10.065