Banach Spaces of Continuous Functions as Dual Spaces

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.

Includes a balance of well-known theorems and applications as well as new research and results Provides a clear account of background information in Stonean spaces, Banach spaces, Banach lattices, Banach algebras, and measure theory Discusses new approaches and syntheses of classical theorem with new examples Includes supplementary material: sn.pub/extras

Contenu
Introduction.- Banach Spaces and Banach Lattices.- Banach Algebras and C* Algebras.- Measures.- Hyper-Stonean Spaces.- The Banach Space.