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 , , 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 . The main results concern properties of the compression Aδ(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 Aδ(z) are established.
|Title of host publication||A Panorama of Modern Operator Theory and Related Topics|
|Subtitle of host publication||The Israel Gohberg Memorial Volume|
|Number of pages||19|
|State||Published - 1 Jan 2012|
- Self-adjoint analytic operator function
- Spectral function
- Spectrum of definite type