**Memoirs of the American Mathematical Society**

2010;
165 pp;
Softcover

MSC: Primary 43;
Secondary 46

Print ISBN: 978-0-8218-4775-6

Product Code: MEMO/205/966

List Price: $78.00

Individual Member Price: $46.80

**Electronic ISBN: 978-1-4704-0580-9
Product Code: MEMO/205/966.E**

List Price: $78.00

Individual Member Price: $46.80

# Banach Algebras on Semigroups and on Their Compactifications

Share this page
*H. G. Dales; A. T.-M. Lau; D. Strauss*

Let \(S\) be a (discrete) semigroup,
and let \(\ell^{\,1}(S)\) be the Banach algebra which is the
semigroup algebra of \(S\). The authors study the structure of
this Banach algebra and of its second dual.

The authors determine exactly when \(\ell^{\,1}(S)\) is
amenable as a Banach algebra, and shall discuss its amenability
constant, showing that there are ‘forbidden values’ for
this constant.

#### Table of Contents

# Table of Contents

## Banach Algebras on Semigroups and on Their Compactifications

- Chapter 1. Introduction 18 free
- Chapter 2. Banach algebras and their second duals 1118 free
- Chapter 3. Semigroups 2734
- Chapter 4. Semigroup algebras 4350
- Chapter 5. Stone--Cech compactifications 5562
- Chapter 6. The semigroup (S, ) 5966
- Chapter 7. Second duals of semigroup algebras 7582
- Chapter 8. Related spaces and compactifications 9198
- Chapter 9. Amenability for semigroups 99106
- Chapter 10. Amenability of semigroup algebras 109116
- Chapter 11. Amenability and weak amenability for certain Banach algebras 123130
- Chapter 12. Topological centres 129136
- Chapter 13. Open problems 149156
- Bibliography 151158
- Index of Terms 159166 free
- Index of Symbols 163170 free