A positive quantization on type I locally compact groups. (English) Zbl 1421.22004
The paper under review considers the natural quantization on unimodular type I second countable locally compact groups as in [M. E. Taylor, Noncommutative microlocal analysis. I. Providence, RI: American Mathematical Society (AMS) (1984; Zbl 0554.35025), V. Fischer and M. Ruzhansky, Quantization on nilpotent Lie groups. New York, NY: Birkhäuser/Springer (2016; Zbl 1347.22001), M. Mantoiu and M. Ruzhansky, Doc. Math. 22, 1539–1592 (2017; Zbl 1403.22006)]. Then analogues of the Berezin quantization and of the Toepliz operators are defined.
Reviewer: Veronique Fischer (Bath)
MSC:
| 22D10 | Unitary representations of locally compact groups |
| 22D25 | \(C^*\)-algebras and \(W^*\)-algebras in relation to group representations |
| 46L80 | \(K\)-theory and operator algebras (including cyclic theory) |
| 47G30 | Pseudodifferential operators |
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