Joint Functional Calculus for Definitizable Self-adjoint Operators on Krein Spaces

摘要

In the present note a spectral theorem for a finite tuple of pairwise commuting, self-adjoint and definitizable bounded linear operators A(1), ... , A(n) on a Krein space is derived by developing a functional calculus phi -> phi (A(1) ,... , A(n)) which is the proper analogue of phi ->integral phi dE in the Hilbert space situation with the common spectral measure E for a finite tuple of pairwise commuting, self-adjoint bounded linear operators.