Normed Spaces and Inner Product Spaces

Abstract

AbstractIn Chapters 2–4 we concerned ourselves primarily with algebraic aspects of certain mathematical systems, while in Chapter 5 we addressed ourselves to topological properties of some mathematical systems. The stage is now set to combine topological and algebraic structures. In doing so, we arrive at linear topological spaces, namely normed linear spaces and inner product spaces, in general, and Banach spaces and Hilbert spaces, in particular. The properties of such spaces are the topic of the present chapter. In the next chapter we will study linear transformations defined on Banach and Hilbert spaces. The material of the present chapter and the next chapter constitutes part of a branch of mathematics called functional analysis.KeywordsHilbert SpaceBanach SpaceLinear SpaceNormed SpaceLinear SubspaceThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.