Abstract. The concept of an elementary operator between two algebras was recently introduced and this paper continues and extends the study of this concept. Elementary operators on some function algebras are computed. Jordan elementary operators are introduced and, in particular, their form on standard operator algebras is described.

AMS Subject Classification (1991): 47B47, 46E25, 16W99

Received December 10, 1999. (Registered under 2767/2009.)