Submanifolds of compact operators with fixed multiplicities of eigenvalues

  • A. A. Bondar
  • Ya. M. Dymarskii Луган. гос. ун-т внутренних дел им. Э. А. Дидоренко


The manifold of symmetric real matrices with fixed multiplicities of eigenvalues was considered for the first time by V. Arnold. In the case of compact real self-adjoint operators, analogous results were obtained by Japanese mathematicians D. Fujiwara, M. Tanikawa, and S. Yukita. They introduced a special local diffeomorphism that maps Arnold's submanifold to a flat subspace. The properties of the indicated diffeomorphism were further studied by Ya. Dymarskii. In the present paper, 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.
How to Cite
Bondar, A. A., and Y. M. Dymarskii. “Submanifolds of Compact Operators With Fixed Multiplicities of Eigenvalues”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, no. 9, Sept. 2011, pp. 1179-8,
Research articles