Banach Function Algebras, Arens Regularity, and BSE Norms

Preface
Acknowledgements
Contents
1 Banach spaces and operators
	1.1 Basic notation
	1.2 Banach spaces
	1.3 Bounded linear operators
	1.4 Tensor products
2 Banach algebras
	2.1 Algebras and Banach algebras
	2.2 C*-algebras and von Neumann algebras
	2.3 Biduals of Banach algebras
	2.4 Dual Banach algebras
3 Banach function algebras
	3.1 Banach function algebras
	3.2 Banach sequence algebras
	3.3 Projective tensor products of Banach function algebras
	3.4 The separating ball property
	3.5 Pointwise approximate identities
	3.6 Uniform algebras and Gleason parts
4 Banach algebras on locally compact groups
	4.1 Group and measure algebras
	4.2 Locally compact abelian groups
	4.3 Fourier and Fourier–Stieltjes algebras
	4.4 Figà-Talamanca–Herz algebras
5 BSE norms and BSE algebras
	5.1 The space L(A) and the algebra mathcalQ(A)
	5.2 Basic definitions and results about BSE norms
	5.3 Examples
	5.4 Pointwise contractive Banach function algebras and ell1-norms
	5.5 Banach function algebras that are ideals in their bidual
6 Arens regularity
	6.1 Topological centres
	6.2 Arens regularity of projective tensor products
	6.3 Biduals of semigroup algebras
	6.4 Arens regularity for algebras on locally compact groups
References
Index of Terms
Index of Theorems and Examples
Index of Symbols