Completely positive hypergroup actions

Completely positive hypergroup actions / Ajit Iqbal Singh.

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Bibliographic Details
Main Author: Singh, Ajit Iqbal, 1944- (Author)
Format: eBook
Language:English
Published: Providence, Rhode Island : American Mathematical Society, 1996.
Series:Memoirs of the American Mathematical Society ; Volume 124, no. 593.
Subjects:
Hypergroups.
Representations of groups.
Measure algebras.
Hypergroups
Measure algebras
Representations of groups
Online Access:Click for online access
Table of Contents:
  • ""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*â€?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 maps2.4. 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 opresentation2.11. 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 positiveâ€?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 2â€?fold absolutely continuous hypergroups""""4.3. Amenability for hypergroups""; ""4.4. Folner hypergroups""; ""4.5. Isometry condition on Î?(Î?)""; ""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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