On representation of Stinespring's type for \(n\)-tuples of completely positive maps in Hilbert \(C^\star\)-modules (Q2262942)

Recall Stinespring's seminal result that any completely positive map \(\varphi\) from a \(C^*\)-algebra \(A\) into the bounded operators \(L(H)\) on a Hilbert space has a representation of the form \(\varphi=S^*\circ\pi\circ S\) for an involutive representation \(\pi\) of \(A\) on \(H\) [\textit{W. F. Stinespring}, Proc. Am. Math. Soc. 6, No. 2, 211--216 (1955; Zbl 0064.36703)]. The paper establishes a representation of this kind for \(n\)-tuples of completely positive maps in Hilbert \(C^*\)-modules.