Completely positive hypergroup actions
About this Title
Ajit Iqbal Singh
Publication: Memoirs of the American Mathematical Society
Publication Year 1996: Volume 124, Number 593
ISBNs: 978-0-8218-0539-8 (print); 978-1-4704-0178-8 (online)
MathSciNet review: 1355035
MSC (1991): Primary 43A10; Secondary 43A35, 43A62, 46L05, 47B49, 47D25
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.
Graduate students and research mathematicians interested in abstract harmonic analysis, functional analysis, and operator theory.
Table of Contents
- 1. Presentations
- 2. Complete positivity and other properties for presentations and opresentations
- 3. Presentations of hypergroups and associated actions
- 4. Some concrete presentations and actions of hypergroups