On a theorem by A. E. Taylor
Shaul R. Foguel · Proceedings of the American Mathematical Society · 1958
Let B be a complex normed linear space. It is well known [l ] that, for any bounded linear functional to B, i.e. a bounded linear functional / defined on B such that (i) f(x) = where \\f\\B and \\4>\\m denote the norms of bounded linear functionals/ and c/> on B and M, respectively. It was proved by A. E. Taylor [2] that if the conjugate space of B is strictly convex, then / is uniquely determined by <p. The purpose of this note is to show that the converse of this theorem is true, i.e. we want to prove the following