| he earliest results on degeneracy of eigenvalues is von Neumann and Wigner's explanation in 1929 why matrices in a one parameter family have, in general, simple eigenvalues: the set of matrices with double eigenvalue form a codimension 2 subvariety. Arnold extended this result to higher multiplicities.;In this work we generalize Arnold's results to the case of operators on a Hilbert space with a parameter being an element of an infinite-dimensional Banach space. Let A(q) be an m times differentiable family of self-adjoint operators on a Hilbert space with discrete spectra and a common domain; the parameter q is an element of a possibly infinite-dimensional Banach space... |
