On subspaces of l and extreme contractions in L(X, lⁿ)

We investigate different possiblities of subspaces of the space l(infinity) in terms of whether the subspaces are polyhedral or not. We further study finite-dimensional subspaces of l(infinity) which are of the form l(infinity)(n) for some n >= 2. As an application of the results we compute the number of extreme contractions for a class of the space of bounded linear operators. In particular we find the number of extreme contractions of L(X, l(infinity)(n) ), where X is a finite-dimensional polyhedral space.