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- Title
Submanifolds of compact operators with fixed multiplicities of eigenvalues.
- Authors
Bondar', A.; Dymarskii, Ya.
- Abstract
For the first time, a manifold of symmetric real matrices with fixed multiplicities of eigenvalues was considered by Arnold. In the case of compact real self-adjoint operators, similar results were obtained by Japanese mathematicians Fujiwara, Tanikawa, and Yukita. They introduced a special local diffeomorphism 'straightening' the Arnold manifold. Later, the properties of the indicated diffeomorphism were studied by Dymarskii. We describe the smooth structure of submanifolds of finite-dimensional and compact operators of the general form in which a selected eigenvalue is associated with a single Jordan block.
- Subjects
SUBMANIFOLDS; COMPACT operators; MULTIPLICITY (Mathematics); EIGENVALUES; MATRICES (Mathematics); SELFADJOINT operators; DIFFEOMORPHISMS
- Publication
Ukrainian Mathematical Journal, 2012, Vol 63, Issue 9, p1349
- ISSN
0041-5995
- Publication type
Article
- DOI
10.1007/s11253-012-0583-7