Chapter 1 Introduction ......................................... 1
Chapter 2 Prerequisites ........................................ 9
2.1 Directed trees ............................................. 9
2.2 Operator theory ........................................... 16
Chapter 3 Fundamental Properties .............................. 19
3.1 An invitation to weighted shifts .......................... 19
3.2 Unitary equivalence ....................................... 24
3.3 Circularity ............................................... 25
3.4 Adjoints and moduli ....................................... 27
3.5 The polar decomposition ................................... 30
3.6 Fredholm directed trees ................................... 32
Chapter 4 Inclusions of Domains ............................... 39
4.1 When is  (Sλ)  (Sλ*)? .................................. 39
4.2 When is (Sλ*) (Sλ)? .................................. 40
4.3 An example ................................................ 46
Chapter 5 Hyponormality and Cohyponormality ................... 49
5.1 Hyponormality ............................................. 49
5.2 Cohyponormality ........................................... 51
5.3 Examples .................................................. 54
Chapter 6 Subnormality ........................................ 57
6.1 A general approach ........................................ 57
6.2 Subnormality on assorted directed trees ................... 64
6.3 Modelling subnormality on  η,k ........................... 70
Chapter 7 Complete Hyperexpansivity ........................... 75
7.1 A general approach ........................................ 75
7.2 Complete hyperexpansivity on η,k ........................ 79
7.3 Modelling complete hyperexpansivity η,k ................. 82
7.4 Completion of weights η,k ............................... 88
7.5 Graph extensions .......................................... 91
Chapter 8 Miscellanea ......................................... 95
8.1 Admissibility of assorted weighted shifts ................. 95
8.2 p-hyponormality ........................................... 98
Bibliography .................................................. 103
List of symbols ............................................... 107
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