On models of function type for a special class of normal operators in Krein spaces and their polar representation - Strauss, V. A. (Methods of Functional Analysis and Topology, 2007)
The paper is devoted to a function model representation of a normal operator N acting in a Krein space. We assume that N and its adjoint operator N^# have a common invariant subspace L_+ which is a maximal nonnegative subspace and has a representation as a sum of a finite-dimensional neutral subspace and a uniformly positive subspace. For N we construct a model representation as the multiplication operator by a scalar function acting in a suitable function space. This representation is applied to the problem of existence of a polar representation for normal operators of D_κ^+-class.