Maximal ideal space of $\mathcal{M}(\mathbb{T})$, the Banach algebra of Borel measures on $\mathbb{T}$ As is well known, the space $\mathcal{M}(\mathbb{T})$ of Borel complex measures on the torus $\mathbb{T}=\{z\in\mathbb{C}:|z|=1\}$ is a (unital) commutative Banach algebra (with total variation as norm and convolution as multiplication). I've been trying to identify the maximal ideal space (that is the complex homomorphisms) of this algebra but so far couldn't even think of a reasonable candidate.
Using the Riesz representation theorem one gets that $\mathcal{M}(\mathbb{T})$ is isommetrical to $C(\mathbb{T})^*$ (the dual of the space of continuous functions from $\mathbb{T}$ to $\mathbb{C}$), so I started trying to figure out the bidual of $C(\mathbb{T})$ expecting it would be a reflexive space. Of course it isn't, but I had forgotten this.
I'm stuck with this. Can someone help me identifying this maximal ideal space? Any reference or idea would be appreciated too.  

It is so complicated that most researchers give up on this problem a long time ago. For details see discussion at section 4.3.14 in Banach and Locally Convex Algebras by A. Ya. Helemskii.
