Extensions of operator valued positive definite functions and commutant lifting on ordered groups (Q5952326)

The authors study the validity of (analogs of) the Kreĭn extension theorem and the Sz.-Nagy-Foias commutant lifting theorem in the framework of ordered groups. For instance, \(\mathbb Z^n\) and \(\mathbb R \times \mathbb Z^n\) with the lexicographic order have the extension property and the commutant lifting property.