Banach spaces of continuous functions as dual spaces

Dales, Harold Garth and Dashiell, F. K. and Lau, Anthony To-Ming and Strauss, D. (2017) Banach spaces of continuous functions as dual spaces. CMS Books in Mathematics . Springer. ISBN 9783319323473

Abstract

This book gives a coherent account of the theory of Banach spaces and Banach lattices, using the spaces C_0(K) of continuous functions on a locally compact space K as the main example. The study of C_0(K) has been an important area of functional analysis for many years. It gives several new constructions, some involving Boolean rings, of this space as well as many results on the Stonean space of Boolean rings. The book also discusses when Banach spaces of continuous functions are dual spaces and when they are bidual spaces.