On spectral functions for commutative J-self-adjoint operator families of the Dκ+-class

Commutative J-self-adjoint operator families of the so-called D-kappa(+)-class in Krein spaces have properties very close to the properties of commutative pi-self-adjoint operator families. On the other hand, the definition of this class does not allow us to check directly if some concrete commutative J-self-adjoint operator family belongs to the class. We describe some properties of the D-kappa(+)-class which give a possibility to verify if an operator family in question is in the class.