Commuting compact self-adjoint operators on a pontryagin space

Abstract

Suppose that A₁,A₂, ..., A_n are compact commuting self-adjoint linear maps on a Pontryagin space K of index k and that their joint root subspace M₀ at the zero eigenvalue in ℂⁿ is a nondegenerate subspace. Then there exist joint invariant subspaces H and F in K such that K=F⊗H,H is a Hilbert space and F is finite-dimensional space with k≤dimF≤(n+2)k. We also consider the structure of restrictions Aj|F in the case k=1.