1 Preliminaries ................................................ 5
1.1 Background .............................................. 5
1.2 Amenability for Banach algebras ......................... 7
1.3 Basic definitions ....................................... 9
1.4 Intrinsic characterizations ............................ 10
1.5 Pointwise variations ................................... 12
1.6 Results concerning ideals .............................. 14
1.7 Banach function algebras ............................... 16
1.8 Banach sequence algebras ............................... 17
1.9 On approximate identities .............................. 25
1.10 Summary of interrelations .............................. 26
2 Semigroup algebras .......................................... 27
2.1 Background ............................................. 27
2.2 The case where E(S) finite ............................. 28
3 A weighted semigroup algebra ................................ 30
3.1 Basic definitions ...................................... 31
3.2 The Gel'fand transform ................................. 32
3.3 An approximate identity ................................ 34
3.4 Weak amenability and amenability ....................... 34
3.5 Pointwise amenability .................................. 35
3.6 Bounded approximate contractibility .................... 36
3.7 Pointwise approximate amenability ...................... 38
3.8 Convergence of 'tails' ................................. 39
3.9 Approximate amenability ................................ 40
3.10 Summary ................................................ 42
3.11 A subsidiary example ................................... 43
4 Segal algebras .............................................. 44
4.1 Introduction ........................................... 44
4.2 The approximate amenability of Segal algebras on  .... 46
4.3 Segal algebras on  ................................... 50
4.4 The pointwise approximate amenability of Segal
algebras on ......................................... 54
4.5 Postscript ............................................. 55
5 Open questions .............................................. 55
References ..................................................... 55
| 
