The order of neutrality for linear operators on inner product spaces Original Research Article

Let A be a symmetric linear operator defined on all of a (possibly degenerate) indefinite inner product space image. Let image be the set of all subspaces of image which are A-invariant, neutral (in the sense of the indefinite scalar product), and finite dimensional. It is shown that members of image which are maximal (with respect to inclusion) all have the same dimension. This is called the “order of neutrality” of A and admits immediate application to self-adjoint operators on a Pontrjagin space.