Denote by $\mathsf{BV}(\mathbb T)$ the Banach space of functions on the circle with bounded variation which is a Banach algebra under the pointwise product. Is there a surjective homomorphism from $\mathsf{BV}(\mathbb T)$ onto $\ell_1(\mathbb Z)$ (with convolution)?

My motivation comes from the fact that Fourier coefficients of functions in $\mathsf{BV}(\mathbb T)$ vanish at infinity however I am not sure if this is directedly related.