Swartz type results for nuclear and multiple 1-summing bilinear operators on $$c_{0}\left( \mathcal {X}\right) \times c_{0}\left( \mathcal {Y}\right) $$.

In this paper we investigate the bilinear versions of Swartz's theorem. Thus we characterize the nuclear and the multiple 1-summing operators on a cartesian product of $$c_{0}\left( \mathcal {X}\right) $$ . As applications we give the necessary and sufficient conditions for some natural operators on a cartesian product of $$c_{0}\left( \mathcal {X}\right) $$ to be multiple 1-summing and nuclear operators. By an example, we show that the natural bilinear version of Swartz's theorem is not necessarily true. [ABSTRACT FROM AUTHOR]