Models of function type for commutative symmetric operator families in Krein spaces (Q938376)

It is the aim of this paper to give a model representation for a commutative family of selfadjoint operators of the class \(D_{\kappa}^+\) acting on a separable Krein space. Here, the model space is a suitable function space such that every member of the above family, restricted to a subspace constructed with the help of the spectral function, is similar to a multiplication operator. The class \(D_{\kappa}^+\) can be considered as one possible generalization of the class of selfadjoint operators in Pontryagin spaces. A family of operators which are selfadjoint with respect to some Krein space inner product is called of \(D_{\kappa}^+\) class if there exists a maximal nonnegative subspace \(\mathcal L\) which is invariant for every member of the family such that its isotropic part is finite-dimensional and \(\mathcal L\) admits a fundamental decomposition into a Krein subspace and its isotropic part.