Robin Harte Dedicated to Goldie Hawn, on her birthday Abstract We attempt to deconstruct the Arens-Royden Theorem. Suppose A is a Banach algebra (by default complex, with identity 1): we shall write 0.1 A−1 = {a ∈ A : 1 ∈ Aa∩aA} for the open subgroup of invertible elements, and A−1 0 for the connected component of the identity in A −1: it turns out ([8], [11] Theorem 7.11.4) that 0.2 A−1 0 = Ex...
