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 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
Mathematics Subject Classification (2000). 47A56, 47A68, 47A10.
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Langer, H., Markus, A., Matsaev, V. (2012). Linearization, Factorization, and the Spectral Compression of a Self-adjoint Analytic Operator Function Under the Condition (VM). In: Dym, H., Kaashoek, M., Lancaster, P., Langer, H., Lerer, L. (eds) A Panorama of Modern Operator Theory and Related Topics. Operator Theory: Advances and Applications(), vol 218. Springer, Basel. https://doi.org/10.1007/978-3-0348-0221-5_20
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DOI: https://doi.org/10.1007/978-3-0348-0221-5_20
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