Extensions and Dilations

1 Extensions and Dilations......Page 1 1.1.2 Direct Approach......Page 2 1.1.3 Computations......Page 3 1.1.4 Parametrization of the Set of Extensions......Page 4 1.2.2 $Z$ as a Convex Set......Page 5 1.3.1 The Definition......Page 6 1.3.2 Representations......Page 7 1.3.3 Construction of Examples......Page 8 1.3.4 The Associated Isometry......Page 9 1.3.5 The Minimal Version of an Associated Isometry......Page 10 1.4.1 An Equivalence Relation......Page 11 1.4.2 Equivalence and Unitary Equivalence......Page 12 1.5.2 From Dilation to Extension......Page 13 1.5.3 From Extension to Dilation......Page 14 1.5.4 One-to-One Correspondence......Page 15 1.5.5 Discussion......Page 16 1.6.2 Adjoints......Page 17 1.6.3 Automorphic Tensor Dilations......Page 18 1.6.4 Duality for Automorphic Tensor Dilations......Page 19 1.7.1 Example 1.1 Revisited......Page 20 1.7.2 Further Discussion......Page 23 1.7.3 A Class of Maps on $M_2$......Page 24 1.7.4 Maps on $M_n$......Page 27