## Abstract

In this paper we continue the study of spectral properties of a selfadjoint analytic operator function A(z) under the Virozub-Matsaev condition. As in [6], [7], main tools are the linearization and the factorization of A(z). We use an abstract definition of a so-called Hilbert space linearization and show its uniqueness, and we prove a generalization of the well-known factorization theorem from [10]. The main results concern properties of the compression A_{δ}(z) of A(z) to its spectral subspace, called spectral compression of A(z). Close connections between the linearization, the inner linearization, and the local spectral function of A(z) and of its spectral compression A_{δ}(z) are established.

Original language | English |
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Title of host publication | A Panorama of Modern Operator Theory and Related Topics |

Subtitle of host publication | The Israel Gohberg Memorial Volume |

Publisher | Springer Basel |

Pages | 445-463 |

Number of pages | 19 |

ISBN (Electronic) | 9783034802215 |

ISBN (Print) | 9783034802208 |

DOIs | |

State | Published - 1 Jan 2012 |

## Keywords

- Factorization
- Linearization
- Self-adjoint analytic operator function
- Spectral function
- Spectrum of definite type