Finite-Codimensional Compressions of Symmetric and Self-Adjoint Linear Relations in Krein Spaces

Theorems due to Stenger (Bull Am Math Soc 74:369-372, 1968) and Nudelman (Int Equ Oper Theory 70:301-305, 2011) in Hilbert spaces and their generalizations to Krein spaces in Azizov and Dijksma (Int Equ Oper Theory 74(2):259-269, 2012) and Azizov et al. (Linear Algebra Appl 439:771-792, 2013) generate additional questions about properties a finite-codimensional compression of a symmetric or self-adjoint linear relation may or may not inherit from . These questions concern existence of invariant maximal nonnegative subspaces, definitizability, singular critical points and defect indices.