Stinespring's theorem for maps on Hilbert \(C^\ast\)-modules (Q2919621)

Stinespring's theorem provides a representation for completely positive maps. It is indeed a natural generalization of the well-known Gelfand-Naimark-Segal theorem for states on \(C^\ast\)-algebras. \textit{M. B. Asadi} [J. Oper. Theory 62, No. 2, 235--238 (2009; Zbl 1199.46128)] proved a Stinespring representation theorem in the setting of Hilbert \(C^\ast\)-modules. The authors of the present work strengthen this result by removing a technical condition and the assumption of unitality of underlying completely positive maps. They also prove uniqueness up to unitary equivalence for minimal representations. Recently, a far-reaching generalization of the paper under review is given by \textit{M. Skeide} [J. Oper. Theory 68, No. 2, 543--547 (2012; Zbl 1274.46114)].