Spectral decomposition of self-adjoint operators in Pontryagin and Krein spaces
Journal: Contemporary Mathematics Fundamental Directions
Year: 2025

We consider a self-adjoint operator acting in a Krein space and possessing an invariant subspace that is maximal nonnegative and decomposes into a direct sum of a uniformly positive (i.e., equivalent to a Hilbert space with respect to the inner pseudoscalar product) and a finite-dimensional neutral subspace. We prove the existence of a difference expression that transforms the moment sequence generated by this operator into a sequence representable as the difference of positive moment sequences.