GLEASON’S THEOREM FOR VECTOR-VALUED MEASURES ON PROJECTORS JBW-ALGEBRAS - A. A. Adizov (Galaxy International Interdisciplinary Research Journal, 2022)
Let JBW algebra [1,2,3] with no direct summand of type ,and let be its lattice of idempotents from and be a Banach space. In this paper, we prove that any finitely additive vector-valued measure has a unique extension to a bounded linear operator mapping to .