Abstract
The concept of a Banach space is a generalization of Hilbert space. A Banach space assumes that there is a norm on the space relative to which the space is complete, but it is not assumed that the norm is defined in terms of an inner product. There are many examples of Banach spaces that are not Hilbert spaces, so that the generalization is quite useful.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1985 Springer Science+Business Media New York
About this chapter
Cite this chapter
Conway, J.B. (1985). Banach Spaces. In: A Course in Functional Analysis. Graduate Texts in Mathematics, vol 96. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-3828-5_3
Download citation
DOI: https://doi.org/10.1007/978-1-4757-3828-5_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4757-3830-8
Online ISBN: 978-1-4757-3828-5
eBook Packages: Springer Book Archive