2017
Том 69
№ 9

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Submanifolds of compact operators with fixed multiplicities of eigenvalues

Bondar A. A., Dymarskii Ya. M.

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Abstract

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.

English version (Springer): Ukrainian Mathematical Journal 63 (2011), no. 9, pp 1349-1360.

Citation Example: Bondar A. A., Dymarskii Ya. M. Submanifolds of compact operators with fixed multiplicities of eigenvalues // Ukr. Mat. Zh. - 2011. - 63, № 9. - pp. 1179-1189.

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