Completely Positive Hypergroup Actions.

Intro -- Contents -- Introduction -- Chapter 1. Presentations -- 1.1. Admissible pairs of normed linear spaces and compatible pairs of Banach spaces -- 1.2. Admissible pairs of spaces of operators -- 1.3. A compatible pair of spaces of functions and measures -- 1.4. Presentations and opresentations -- 1.5. Actions and opactions -- Chapter 2. Complete Positivity and Other Properties for Presentations and Opresentations -- 2.1. The C*-algebra M[sub(n)](A) and completely positive maps -- 2.2. Matrix ordered and matricially normed spaces -- 2.3. Matrix ordered and matricially normed spaces of linear maps -- 2.4. Interconnections amongst different notions of positivity and complete positivity -- 2.5. Matricially order or norm admissible and compatible pairs -- 2.6. Examples of matricially norm admissible and compatible pairs -- 2.7. Matricially order or norm admissible and compatible pairs of spaces of linear maps -- 2.8. Completely positive and completely bounded presentations and opresentations -- 2.9. Topological structures on spaces of presentations -- 2.10. Properties of the dual presentation and opresentation -- 2.11. Completely positive and completely bounded actions and opactions -- 2.12. Examples and remarks -- Chapter 3. Presentations of Hypergroups and Associated Actions -- 3.1. (M(K), C[sub(b)]K)) as a natural matricially order compatible pair -- 3.2. Matricially order compatible structures on (M(K), C[sub(b)]K)) through representations -- 3.3. Special matrix orders on M(K) for commutative K -- 3.4. Role of conjugate representations in Fourier transform -- 3.5. Positive definite presentations and completely positive opresentations of hypergroups -- 3.6. The spectral subspaces of a presentation of a hypergroup -- 3.7. Quantized positive-definite presentations and opresentations of hypergroups.

3.8. Completely positive instruments with values in K and their characteristic functions -- 3.9. Completely positive hypergroup actions and opactions -- Chapter 4. Some Concrete Presentations and Actions of Hypergroups -- 4.1. Presentations and opresentations arising from the left regular representation -- 4.2. The situation in 2-fold absolutely continuous hypergroups -- 4.3. Amenability for hypergroups -- 4.4. Folner hypergroups -- 4.5. Isometry condition on Λ(μ) -- 4.6. Actions and opactions arising from the left regular representation -- 4.7. The special case X = L[sup(2)](K) = X[sub(*)] -- References.

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