Quasitriangular operator algebras

Abstract

Fix a sequence ^ = {P n }"=i of finite dimensional projections increasing to the identity on a separable Hubert space W and let j?(2f) denote the algebra of all bounded operators on 5K. The quasitriangular algebra associated with $P and denoted as 3~(&) is defined to be the set of those operators T in i?($?) for which || Pt TP n ||-0.