Let $ \mathcal{A} =\left\{f \in C(\mathbb{T}): \forall n \in \mathbb{N}^{+}, \int_{0}^{2 \pi} f\left(e^{i \theta}\right) e^{i n \theta} \mathrm{d} \theta=0\right\}$.prove $ \mathcal{A}$ is a banach algebra and find its maximal ideal space
I have aleady prove $ \mathcal{A}$ is a banach algebra,but I don’t know how to find its maximal ideal space ,hope you can give me some methods to fix it