Models of Function Type for Commutative Symmetric Operator Families in Krein Spaces

Abstract

Commutative symmetric operator families of the so-called $D_{\kappa }^{+}$-class are considered in Krein spaces. It is proved that the restriction of a family of this type on a special kind of invariant subspace is similar to a family of operators adjoint to multiplication operators by scalar functions acting on a suitable function space.