Representations of chordal subalgebras of von Neumann algebras (Q749826)

The objective of this note is to generalize the notion of ``chordal'' introduced recently for subalgebras of \(M_ n\) linearly spanned by the matrix units it contains to the context of von Neumann algebras M and to show if \({\mathcal F}\) is a \(\sigma\)-weakly closed subalgebra of M and if \({\mathcal F}\) is chordal triangular subalgebra and if M is hyperfinite, then every \(\sigma\)-weakly contractive representation of \({\mathcal F}\) is completely contractive.