Abstract
The main objective of this chapter is to present an outline of the basic tools of analysis necessary to develop the subsequent chapters. The results addressed include the open mapping and closed graph theorems and an introduction to Hilbert spaces. We assume the reader has a background in linear algebra and elementary real analysis at an undergraduate level.
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
G. Bachman, L. Narici, Functional Analysis (Dover Publications, New York, 2000)
M. Reed, B. Simon, Methods of Modern Mathematical Physics, Volume I, Functional Analysis (Reprint Elsevier, Singapore, 2003)
W. Rudin, Functional Analysis, 2nd edn. (McGraw-Hill, New York, 1991)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Botelho, F. (2014). Topological Vector Spaces. In: Functional Analysis and Applied Optimization in Banach Spaces. Springer, Cham. https://doi.org/10.1007/978-3-319-06074-3_1
Download citation
DOI: https://doi.org/10.1007/978-3-319-06074-3_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-06073-6
Online ISBN: 978-3-319-06074-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)