Abstract: | 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 ({T_0}) of a symmetric or self-adjoint linear relation ({T}) may or may not inherit from ({T}). These questions concern existence of invariant maximal nonnegative subspaces, definitizability, singular critical points and defect indices. |