Let A be a symmetric linear operator defined on all of a (possibly degenerate) indefinite inner product space ℋ. Let script N sign be the set of all subspaces of ℋ which are A-invariant, neutral (in the sense of the indefinite scalar product), and finite dimensional. It is shown that members of script N sign 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.
ASJC Scopus subject areas
- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics