Cominimal projections in \(l_\infty^n\) (Q1279883)

The paper investigates the constant \(\lambda_I(Y,l^n_\infty)\), the infimum of \(\|I-P\|\) over all linear projections \(P\) of \(l^n_\infty\) onto \(Y\), where \(Y\) is a subspace of \(l^n_\infty\) of codimension two; a projection \(P\) is cominimal if \(\|I-P\|=\lambda_I (Y,l^n_\infty)\). Those \(Y\) such that \(\lambda_I(Y,l^n_\infty)=1\) are completely characterised. For \(Y\) such that \(\lambda_I(Y,l^n_\infty)>1\) an estimate from below is obtained. Illustrative examples in the cases \(n=3,4,5,7\) are calculated.