Joint functional calculus for definitizable self-adjoint operators on Krein spaces (Q786082)

The intricate nature of commuting systems of self-adjoint operators acting on a Hilbert space imposes additional rather restrictive consitions (commutations of the associated spectral measures) for posessing a joint spectral (measure) decomposition. This phenomenon is taken by the authors to the very delicate setting of unbounded linear operators acting on a space endowed with an indefinite metric. The single operator case is classical, due to a foundational work of \textit{H. Langer} [Lect. Notes Math. 948, 1--46 (1982; Zbl 0511.47023)]. The authors find the natural generalization of Langer's Theorem to the case of a tuple of definitizable self-adjoint operators on Krein space. The resulting functional calculus is restricted to a class of measurable functions defined on the joint spectrum and the fibres (zero locus) of some distinguished polynomials. A spectral projection theorem is derived.