Abstract
Normed spaces are treated at length as well as techniques of Banach spaces for solving differential and integral equations. Classical results, such as the Open Mapping Theorem, the Closed Graph Theorem, the Hahn-Banach Theorem, the Riesz Representation Theorem, and a few more, are given as well, establishing the core of the theory of bounded operators on Banach spaces. The chapter closes with a view towards generalizations of the theory in two directions, providing a glimpse of the theory of unbounded operators and of locally convex spaces.
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
References
C.D. Aliprantis, K.C. Border, Infinite Dimensional Analysis (A Hitchhiker’s Guide), Third edn. (Springer, Berlin, 2006), p. 703
N.L. Carothers, A Short Course on Banach Space Theory, London Mathematical Society Student Texts (Cambridge University Press, Cambridge, 2005), vol. 64, p. 184
M.S. Osborne, Locally Convex Spaces, Graduate Texts in Mathematics (Springer, Cham, 2014), vol. 269, p. 213
G.K. Pedersen, Analysis Now, Graduate Texts in Mathematics (Springer, New York, 1989), vol. 118, p. 277
K. Yosida, Functional Analysis, Classics in Mathematics (Springer, Berlin, 1995), p. 501
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Alabiso, C., Weiss, I. (2015). Normed Spaces. In: A Primer on Hilbert Space Theory. UNITEXT for Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-03713-4_5
Download citation
DOI: https://doi.org/10.1007/978-3-319-03713-4_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-03712-7
Online ISBN: 978-3-319-03713-4
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)