Abstract
The first two paragraphs are concerned with methods of producing new locally convex spaces from given ones. Thus subspaces and quotient spaces of locally convex spaces are again locally convex. The same holds for topological products and locally convex direct sums. The completion of a locally convex space is obtained in a simple way by embedding the space in a topological product of Banach spaces.
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
© 1983 Springer-Verlag Berlin, Heidelberg
About this chapter
Cite this chapter
Köthe, G. (1983). Locally Convex Spaces. Fundamentals. In: Topological Vector Spaces I. Grundlehren der mathematischen Wissenschaften, vol 159. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-64988-2_4
Download citation
DOI: https://doi.org/10.1007/978-3-642-64988-2_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-64990-5
Online ISBN: 978-3-642-64988-2
eBook Packages: Springer Book Archive