1 Introduction ................................................. 5
2 Multipliers .................................................. 7
2.1 For Banach algebras ..................................... 9
2.2 Extending module actions and homomorphisms ............. 13
2.3 Tensor products ........................................ 14
3 When we have a bounded approximate identity ................. 16
3.1. Smaller submodules ..................................... 18
4 Dual Banach algebras ........................................ 22
5 Self-induced Banach algebras ................................ 23
6 Completely contractive Banach-algebras ...................... 28
6.1. For the Fourier algebra ................................ 31
7 When multiplier algebras are dual ........................... 33
7.1 For dual Banach algebras ............................... 36
7.2 When we have a bounded approximate identity ............ 37
8 Application to locally compact quantum groups ............... 39
8.1 Completely bounded multipliers ......................... 43
8.2 Duality and multipliers ................................ 44
9 Multiplier Hopf convolution algebras ........................ 50
9.1 Haagerup tensor products ............................... 50
9.2 Multiplier algebras .................................... 52
9.3 Application to corepresentations ....................... 55
9.4 Avoiding multipliers ................................... 58
10 Weak topologies ............................................. 58
References ..................................................... 59
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