Anzeige
Erschienen in:
2018 | OriginalPaper | Buchkapitel
4. Normed Spaces
verfasst von : Sergei Ovchinnikov
Erschienen in: Functional Analysis
Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
Abstract
The first two sections of this chapter are concerned with basic properties of normed spaces and linear operators on them. The concept of a Schauder basis is central in Section 4.1. These bases are useful tools in investigating sequence spaces and linear functionals on them. Section 4.2 is concerned mostly with bounded operators and the space of bounded operators from a normed space into another normed space. The central result of this section establishes the equivalence of continuity and boundedness of a linear operator. Although the concept of the dual space is introduced in Section 4.2, we postpone studies of linear functionals and duality until Chapter 5. Several examples of linear operators are also presented in Section 4.2.