Closed one-sided ideals in certain $B^{\ast}$-algebras

Abstract

BRC A. BAR.as B with the property that lim.(I E,,)E, 0 for every fixed m, then is culled an admissible sequence.In particular any decreasing sequence of projections is admissible.We denote the set of all admissible sequences of projections in B as 8.If {E} and {G} are in $, we define {E} G} if lim (I G,,)E, 0 for every m.PnOeOSTON 2.1.<_ is reflexive and transitive on $.Proof.Reflexivity is immediate since every sequence in $ is admissible.Now assume that G}, {F}, {E} e S, and {G} <_ {F} and {Fn} _ _ {En}.