Dales H.G., Dashiell Jr.F.K, Lau A.T.-M., Strauss D. Banach Spaces of Continuous Functions as Dual Spaces

Springer International Publishing, Switzerland, 2016. — 286 p. — (CMS Books in Mathematics) — ISBN10: 3319323474This 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.Banach Spaces and Banach Lattices
Banach Algebras and C∗-Algebras
Measures
Hyper-Stonean Spaces
The Banach Space C(K)