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Erschienen in:
2022 | OriginalPaper | Buchkapitel
1. Preliminaries
verfasst von : Marinus A. Kaashoek, Sjoerd M. Verduyn Lunel
Erschienen in: Completeness Theorems and Characteristic Matrix Functions
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Abstract
This chapter has an introductory character. Basic elements of operator theory are reviewed, and the notion of completeness is defined for Banach space operators and specified further for Hilbert space operators. Elements of spectral theory are presented, and a few illustrative examples are given. The chapter consists of three sections of which the first consists of four subsections. Throughout the Banach and Hilbert spaces are assumed to be complex spaces.