Projections in the J-sums of Banach spaces

Abstract

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