Structure of a family of commuting J-self-adjoint operators (Q914134)

The starting point of the paper is a theorem involving some properties of the J-spectral function of an arbitrary operator \(A\in {\mathfrak D}\), where \({\mathfrak D}\) is the commutable family of the J-selfadjoint operators with the same maximal non-negative invariant subspace which is a direct sum of a uniform positive subspace and a finite-dimensional neutral subspace (the general frame being that of a separable Hilbert space as usually resulting from a Krein space by the fundamental symmetry J). The author studies the problem of modelling such a J-spectral function, and generalizes some of the own previously published results concerning the \(\pi\)-selfadjoint operators.