Minimal projections onto subspaces of \(l_ \infty^{(n)}\) of codimension two (Q1333001)

Let \(Y\subset \ell^{(n)}_ \infty\) be a subspace of codimension two. Denote by \({\mathcal P}_ Y\) the set of all linear projections going from \(\ell^{(n)}_ \infty\) onto \(Y\). Put \(\lambda_ Y= \inf\{\| P\|: P\in {\mathcal P}_ Y\}\). An operator \(P_ 0\in {\mathcal P}_ Y\) is called a minimal projection if \(\| P_ 0\|= \lambda_ Y\). We present a partial solution of the problem of calculation \(\lambda_ Y\) as well as the problem of calculation minimal projection. We also characterize the uniqueness of minimal projection.