Single elements in Banach algebras

This paper provides an abstract characterization of quasitriangular algebras of operators on a separable Hilbert space. The main tool used is the (purely algebraic) concept of a single element. An element s of an algebra A is called single element of A if whenever asb = 0 for some a, b in A, at least one of as, sb is zero. A part of this work is of independent interest and this is an attempt to determine an involution in a Banach algebra.  2002 Elsevier Science (USA). All rights reserved