Let  be the disc algebra, i.e., the uniform algebra of functions analytic on open unit disc  and continuous on its closure. In this paper, we first consider a weighted composition operator on  of the form

where  and  and study its nuclearity. Then we consider a weighted composition operator on Banach algebra (the space of all continuous complex valued functions on compact Hausdorff space X, equipped with supnorm) and give a nuclearity criterion for this operator.

weighted composition operator, nuclear operator.