CONTENTS
Introduction xi
Chapter 1. Presentations 1
1.1. Admissible pairs of normed linear spaces and compati-
ble pairs of Banach spaces 1
1.2. Admissible pairs of spaces of operators 1
1.3. A compatible pair of spaces of functions and measures 2
1.4. Presentations and opresentations 3
1.5. Actions and opactions 6
Chapter 2. Complete Positivity and Other Properties for Pre-
sentations and Opresentations 8
2.1. The C*-algebra Mn(A) and completely positive maps 8
2.2. Matrix ordered and matricially normed spaces 9
2.3. Matrix ordered and matricially normed spaces of linear
maps 11
2.4. Interconnections amongst different notions of positivity
and complete positivity 14
2.5. Matricially order or norm admissible and compatible
pairs 17
2.6. Examples of matricially norm admissible and compat-
ible pairs 18
2.7. Matricially order or norm admissible and compatible
pairs of spaces of linear maps 19
2.8. Completely positive and completely bounded presenta-
tions and opresentations 21
2.9. Topological structures on spaces of presentations 23
2.10. Properties of the dual presentation and opresentation 24
2.11. Completely positive and completely bounded actions
and opactions 25
2.12. Examples and remarks 30
Chapter 3. Presentations of Hypergroups and Associated Ac-
tions 31
3.1. (3ft(K), Cb{K)) as a natural matricially order compat-
ible pair 32
3.2. Matricially order compatible structures on (M(K),
Cb(K)) through representations 34
3.3. Special matrix orders on M(K) for commutative K 36
3.4. Role of conjugate representations in Fourier transform 37
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