Inspired by the classical Bohman-Korovkin-Wulbert (BKW) operators, we initiate a study of noncommutative BKW-operators. Let A be a unital \(C^{*}\) -algebra, and S be a set of generators of A. A unital completely positive (UCP)-map \(\phi : A\rightarrow B(H)\) is said to be a noncommutative BKW-operator for S with respect to norm or weak operator topology (WOT) or strong operator topology (SOT) if for any sequence of UCP-maps \(\phi _n:A\rightarrow B(H)\) , \(n=1,2,...,\) \(\lim _{n\rightarrow \infty }\phi _n(s)=\phi (s),\forall ~s\in S\) in norm (or WOT or SOT) \(\Rightarrow \lim _{n\rightarrow \infty }\phi _n(a)=\phi (a), \forall ~a\in A\) in norm (or WOT or SOT, respectively). We identify a connection between noncommutative BKW-operators and the unique CP-extension of UCP-maps. We have discussed several examples and explored different notions of noncommutative BKW-operators and their interconnections. Additionally, we introduce the concept of hyperrigidity with respect to a UCP-map and characterize it along the lines of Arveson. Although independent yet related to noncommutative BKW-operators, we provide a noncommutative version of the operator version of the Korovkin theorem recently proposed by D. Popa.
