Spectral subspaces and non-commutative Hilbert transforms (Q2773274)

Let \(G\) be a locally compact Abelian group and \({\mathcal M}\) be a semifinite von Neumann algebra with a faithful semifinite normal trace. In the paper are studied Hilbert transforms associated with \(G\)-flows on \({\mathcal M}\) and closed semigroups \(\Sigma\) of \(\widehat G\) satisfying the condition \(\Sigma\cup(-\Sigma)=\widehat G\) and is proved a non-commutative weak-type estimate that generalizes the celebrated Kolmogorov result. As an application is proved a Matsaev-type result for \(p= 1\). The details are two technical to be stated here.