| Abstract: | Given a Banach space  , we have shown in 1994 that a product can be defined on it in such a way that the resulting Banach algebra is isomorphic to a compact subalgebra of the algebra  of all bounded linear operators on the topological dual  of  . Our purpose here is to prove that, more generally, any Banach algebra  admitting a left approximate identity, is isomorphic to a subalgebra of  , the isomorphism being isometric, provided the approximate identity is bounded by 1. As a consequence, we get a factorization through  , of the elements in  . |
