On Unitary Equivalence of Matrices over the Ring of Continuous Complex-Valued Functions on a Stonian Space

This paper is a continuation of the earlier papers (1, 5) in which the author studied matrices with entries from the algebra C() of all continuous, complex-valued functions on an extremely disconnected, compact Hausdorff space . (Such spaces are sometimes called Stonian, after M. H. Stone, who first considered them in (8). They arise naturally as maximal ideal spaces of abelian W*-algebras.) In this note, three theorems are proved.