Completely continuous Banach algebras

with n1; : : : ; nk in N. A Banach algebra with the above representation is usually called trivial. In that paper , they proved that every re exive, amenable Banach algebra for which all primitive ideals have nite codimension is trivial. In the same year B. E. Johnson proved that every re exive, amenable Banach algebra whose maximal left ideals are complemented is trivial (see also, ).