ON STABILITY OF C-ASTERISK-ALGEBRAS

Let A be a sigma-unital C-algebra, i.e., A admits a countable approxi mate unit. It is proved that A is stable, i.e., A is isomorphic to AxH where H is the algebra of compact operators on a separable Hilbert sp ace, if and only if for each positive element a is an element of A and each epsilon>0 there exists a positive element b is an element of A s uch that parallel to ab parallel to<epsilon and xx = a, xx* = b for s ome x in A. Using this characterization it is proved among other thing s that the inductive limit of any sequence of sigma-unital stable C-a lgebras is stable, and that the crossed product of a sigma-unital stab le C-algebra by a discrete group is again stable. (C) 1998 Academic P ress.