ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 47B50 Strauss, Vladimir, USB, Caracas, Venezuela & SUSU, Chelyabinsk, Russia On a model representation for a normal operator in Krein space The present report is devoted to a functional model representation of a normal operator N acting in a Krein space. We suppose that N and its adjoint operator N^{[∗]} have a common invariant subspace L^{+} which is a maximal nonnegative subspace that can be represented as a direct sum of a finite-dimensional neutral subspace and a uniformly positive subspace. We construct for N a model representation as the operator of multiplication by the independent variable acting in some functional space. Reference: Azizov, T. Ya and Iokhvidov, I. S. Linear Operators in Spaces with Indefinite Metric, Wiley, New York, 1989.