A Banach space which is not reflexive may or may not be equivalent (in Banach's sense) to an adjoint space. For example, it is an elementary fact that the space (l), though not reflexive, is equivalent to (co)*, where (co) is the space of all sequences that converge to zero, normea in the usual way. On the other hand, (co) itself is not equivalent to any adjoint space : this can be proved by means of the Krein-Milman theorem, but here we obtain the result by an elementary argument which is scarcely more complicated than the standard proof that (co) is not reflexive.