Abstract :
Let B be a monotone σ -complete C∗-algebra. Let (μn) (n = 1, 2, . . .) be a sequence in the dual of
B such that limμn(p) exists for each projection p.We prove that the sequence must converge weakly.
As an application, we obtain a non-commutative generalisation of the Brooks–Jewett Theorem.
2004 Elsevier Inc. All rights reserved.
