A Course on Topological Vector Spaces (1st ed. 2020) (Compact Textbooks in Mathematics)
By:
Sign Up Now!
Already a Member? Log In
You must be logged into Bookshare to access this title.
Learn about membership options,
or view our freely available titles.
- Synopsis
- This book provides an introduction to the theory of topological vector spaces, with a focus on locally convex spaces. It discusses topologies in dual pairs, culminating in the Mackey-Arens theorem, and also examines the properties of the weak topology on Banach spaces, for instance Banach’s theorem on weak*-closed subspaces on the dual of a Banach space (alias the Krein-Smulian theorem), the Eberlein-Smulian theorem, Krein’s theorem on the closed convex hull of weakly compact sets in a Banach space, and the Dunford-Pettis theorem characterising weak compactness in L1-spaces. Lastly, it addresses topics such as the locally convex final topology, with the application to test functions D(Ω) and the space of distributions, and the Krein-Milman theorem. The book adopts an “economic” approach to interesting topics, and avoids exploring all the arising side topics. Written in a concise mathematical style, it is intended primarily for advanced graduate students with a background in elementary functional analysis, but is also useful as a reference text for established mathematicians.
- Copyright:
- 2020
Book Details
- Book Quality:
- Publisher Quality
- ISBN-13:
- 9783030329457
- Related ISBNs:
- 9783030329440
- Publisher:
- Springer International Publishing
- Date of Addition:
- 05/27/20
- Copyrighted By:
- Springer
- Adult content:
- No
- Language:
- English
- Has Image Descriptions:
- No
- Categories:
- Nonfiction, Mathematics and Statistics
- Submitted By:
- Bookshare Staff
- Usage Restrictions:
- This is a copyrighted book.