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Completely Positive Hypergroup Actions
Ajit Iqbal Singh, University of Delhi, India
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Memoirs of the American Mathematical Society
1996; 68 pp; softcover
Volume: 124
ISBN-10: 0-8218-0539-8
ISBN-13: 978-0-8218-0539-8
List Price: US$40
Individual Members: US$24
Institutional Members: US$32
Order Code: MEMO/124/593
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It is now well known that the measure algebra \(M(G)\) of a locally compact group can be regarded as a subalgebra of the operator algebra \(B(B(L^2(G)))\) of the operator algebra \(B(L^2(G))\) of the Hilbert space \(L^2(G)\). In this memoir, the author studies the situation in hypergroups and finds that, in general, the analogous map for them is neither an isometry nor a homomorphism. However, it is completely positive and completely bounded in certain ways. This work presents the related general theory and special examples.

Readership

Graduate students and research mathematicians interested in abstract harmonic analysis, functional analysis, and operator theory.

Table of Contents

  • Presentations
  • Complete positivity and other properties for presentations and opresentations
  • Presentations of hypergroups and associated actions
  • Some concrete presentations and actions of hypergroups
  • References
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