EXTREME-POINTS IN TRIANGULAR UHF ALGEBRAS

We examine the strongly extreme point structure of the unit balls of t riangular UHF algebras. The semisimple triangular UHF algebras are cha racterized as those for which this structure is minimal in the sense t hat every strongly extreme point belongs to the diagonal. In contrast to this, for the class of full nest algebras we prove a Krein-Milman t ype theorem which asserts that every operator in the open unit ball of the algebra is a convex combination of strongly extreme points.