Change of Jordan structure of G-selfadjoint operators and selfadjoint
operator functions under small perturbations
Vadim Olshevsky
In 1980 Markus and Parilis, and den Boer and Thijsse,
confirming an earlier conjecture of Gohberg and Kaashoek,
obtained a
description of the possible domain of variation of the lengths of Jordan
chains ( partial multiplicities )
of linear operators and analytic operator functions, and of
Gohberg-Kaashoek numbers,
under small perturbations. In this paper similar problems are
extended to the classes of G-selfadjoint operators, and selfadjoint
operator functions. For this case, we obtained new inequalities on the variation of
partial multiplicities, revealing the role played by
the sign characteristic.
Related papers:
Two new proofs for the Markus-Parilis-den Boer-Thijsse theorem, which are
based on the analysis of cyclic dimensions and of
kernel multiplicities, appeared in
[MO94]. The role played by the
Gohberg-Kaashoek numbers in the description of the behavior of
the lattice of all invariant subspaces, under a small perturbation of
a matrix, is revealed in [O89a].
Vadim Olshevsky's Home page
Vadim Olshevsky
olshevsk@isl.stanford.edu
Last modified: Fri Sep 15 1995