Abstract
Various collections of functions carry the structure of a vector space, and functional analysis is devoted to the study of such vector spaces, mainly from an analytic rather than linear algebraic perspective. When working with vector spaces, one is required to specify the underlying base field. In analysis, the natural choices are the fields \(\mathbb{R}\) and \(\mathbb{C}\), which are preferable to the field \(\mathbb{Q}\) or some finite field \(\mathbb{F}\), because of the completeness properties enjoyed by the real and complex fields.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Farenick, D. (2016). Banach Spaces. In: Fundamentals of Functional Analysis. Universitext. Springer, Cham. https://doi.org/10.1007/978-3-319-45633-1_5
Download citation
DOI: https://doi.org/10.1007/978-3-319-45633-1_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-45631-7
Online ISBN: 978-3-319-45633-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)