Electronic ISBN:  9781470405809 
Product Code:  MEMO/205/966.E 
List Price:  $78.00 
MAA Member Price:  $70.20 
AMS Member Price:  $46.80 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 205; 2010; 165 ppMSC: Primary 43; Secondary 46;
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

Chapters

1. Introduction

2. Banach algebras and their second duals

3. Semigroups

4. Semigroup algebras

5. Stone–Čech compactifications

6. The semigroup $(\beta S, \Box )$

7. Second duals of semigroup algebras

8. Related spaces and compactifications

9. Amenability for semigroups

10. Amenability of semigroup algebras

11. Amenability and weak amenability for certain Banach algebras

12. Topological centres

13. Open problems


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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.

Chapters

1. Introduction

2. Banach algebras and their second duals

3. Semigroups

4. Semigroup algebras

5. Stone–Čech compactifications

6. The semigroup $(\beta S, \Box )$

7. Second duals of semigroup algebras

8. Related spaces and compactifications

9. Amenability for semigroups

10. Amenability of semigroup algebras

11. Amenability and weak amenability for certain Banach algebras

12. Topological centres

13. Open problems