Remarks on the interpolation and the similarity problem for nest subalgebras of von Neumann algebras (Q1892239)

Given a nest subalgebra of a von Neumann algebra \({\mathcal A}\) and vectors \(f\), \(g\) the author gives necessary and sufficient conditions for the existence of an operator \(A\) in \({\mathcal A}\) so that \(Af =g\). This generalizes a well-known theorem of E. C. Lance and the main result in \textit{M. Anoussis} [Proc. Am. Math. Soc. 114, No. 3, 707-710 (1992; Zbl 0780.47029)]; \textit{E. G. Katsoulis}, \textit{R. L. Moore} and \textit{T. T. Trent} [J. Oper. Theory 29, 115-123 (1993; Zbl 0813.47053)]. We also use the generalized Ringrose criterion to show that the similarity problem for continuous nests in certain crossed product factors of type III has a negative answer.