Factorizations of operator-valued functions on ordered groups
Sz. Nagy and Foias used an approach based upon the Wold decomposition of an isometry for proving factorization results for operator-valued functions on the unit circle. We are applying an analogue of the Wold decomposition for semigroups of isometries to give some geometric insight into factorization results by Helson and Lowdenslager for matrix-valued functions defined on compact groups with a totally ordered dual. By using some counterexamples, we show that the extensions of these results to operator- valued functions face some basic obstructions. The talk is based on joint work with Dan Timotin (Mathematical Institute of the Romanian Academy).
