Operator moment theorems for C *-algebras (Q1096868)

Let A be a C *-algebra, G a subset of A closed under multiplication and involution and whose linear span is norm-dense in A, and B(H) the algebra of bounded linear operators on a Hilbert space H. In the paper under review, the author gives (Theorem 1) necessary and sufficient conditions for a function \(f: G\to B(H)\) to have a positive linear extension to A. This result extends (and uses) an earlier, similar result of the author [Acta Math. Hung. 42, 331-335 (1983; Zbl 0556.46035)] on scalar-valued functions. The author also gives a proof (Theorem 2), based on an inequality in [\textit{R. V. Kadison}, Ann. Math., II. Ser. 56, 494-503 (1952; Zbl 0047.357)], of a non-normalized Naimark dilation theorem [see \textit{S. K. Berberian}, Mich. Math. J. 13, 171-184 (1966; Zbl 0152.138)], and applies Theorems 1 and 2 to the case where A is a commutative C *- algebra.