Complemented subspaces of $J$-sums of Banach spaces

We study the complemented subspaces of the $J$-sums of Banach spaces $J(\mathrm{\Phi })$ and $\widehat{J}(\mathrm{\Phi })$ introduced by Bellenot. As an application, we show that, under some conditions, $J(\mathrm{\Phi })$ and $\widehat{J}(\mathrm{\Phi })$ are subprojective, i.e., every closed infinite-dimensional subspace of either of them contains a complemented infinite-dimensional subspace.