On models of function type for a special class of normal operators in Krein spaces and their polar representation

Abstract

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.

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Article Information

Title	On models of function type for a special class of normal operators in Krein spaces and their polar representation
Source	Methods Funct. Anal. Topology, Vol. 13 (2007), no. 1, 67-82
MathSciNet	MR2308581
Copyright	The Author(s) 2007 (CC BY-SA)

Authors Information

Vladimir Strauss
Department of Pure and Applied Mathematics, Simon Bolivar University, SartenejasBaruta, Apartado 89.000, Caracas 1080A, Venezuele

Citation Example

Vladimir Strauss, On models of function type for a special class of normal operators in Krein spaces and their polar representation, Methods Funct. Anal. Topology 13 (2007), no. 1, 67-82.

BibTex

@article {MFAT373,
    AUTHOR = {Strauss, Vladimir},
     TITLE = {On  models of function type for a special class of normal operators in Krein spaces and their polar representation},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {13},
      YEAR = {2007},
    NUMBER = {1},
     PAGES = {67-82},
      ISSN = {1029-3531},
  MRNUMBER = {MR2308581},
       URL = {http://mfat.imath.kiev.ua/article/?id=373},
}