ON MODELS OF FUNCTION TYPE FOR A SPECIAL CLASS OF NORMAL OPERATORS IN KREIN SPACES AND THEIR POLAR REPRESENTATION

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(kappa)(+-)class.