EAN: 9783030329440

COMPACT TEXTBOOKS IN MATHEMATICS A COURSE ON ...

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( ) 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.

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