On intersections of ranges of projections of norm one in Banach spaces (Q2845433)

This paper is devoted to the study of finite-dimensional projections of norm one in Banach spaces. In particular, the author analyzes for which Banach spaces the range of any norm one projection with finite-dimensional kernel is an intersection of ranges of norm one projections with one-dimensional kernels. He also investigates a kind of converse to the above, namely, when finite intersections of ranges of norm one projections with one-dimensional kernel are again the range of a norm one projection. Several results are given, relating these questions with \(M\)-ideals, central subspaces and \(L^1\)-preduals. These illustrate and generalize known results for projections on \(c_0\), \(\ell_\infty\) and \(C(K)\). The reader is referred to the interesting paper for details.