Can we turn $M(X, \Sigma)$ into a Banach algebra?

Question

If $(X, \Sigma)$ is a measurable space and $M(X, \Sigma)$ denotes the set of all complex measures on $\Sigma$. Then we know that $M(X, \Sigma)$ is a Banach space with respect to the total variation norm $\|.\|$(https://en.wikipedia.org/wiki/Total_variation). Can we define an associative, bilinear map $M(X, \Sigma) \times M(X, \Sigma) \to M(X, \Sigma)$, satisfying $\|\mu \cdot \nu\| \leq \|\mu\|\|\nu\|$ for all $\mu, \eta \in M(X,\Sigma)$ and such that this operation is non-trivial (meaning that there exist $\mu, \nu$ such that $\mu \cdot \nu \neq 0$, where 0 denotes the zero-measure in that case) ? To rephrase it again, can we turn $M(X, \Sigma)$ into a Banach algebra without defining the multiplication to be always $0$?