THE ORDER OF NEUTRALITY FOR LINEAR-OPERATORS ON INNER-PRODUCT SPACES

Let A be a symmetric linear operator defined on all of a (possibly deg enerate) indefinite inner product space H. Let N be the set of all sub spaces of H which are A-invariant, neutral (in the sense of the indefi nite scalar product), and finite dimensional. It is shown that members of N 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. (C) Elsevier Science Inc., 1997.