Markov dilations of semigroups of Fourier multipliers. (English) Zbl 1504.47022
Summary: We describe a Markov dilation for any weak\(*\) continuous semigroup \((T_t)_t \geqslant 0\) of selfadjoint unital completely positive Fourier multipliers acting on the group von Neumann algebra \(\mathrm{VN}(G)\) of a locally compact group \(G\).
MSC:
| 47A20 | Dilations, extensions, compressions of linear operators |
| 47D03 | Groups and semigroups of linear operators |
| 46L51 | Noncommutative measure and integration |
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