Extreme and smooth points in lorentz and marcinkiewicz spaces with applications to contractive projections

We characterize extreme and smooth points in the Lorentz sequence space d(w, 1) and in Marcinkiewicz sequence spaces d*(w, 1) and d*(w, 1), which are predual and dual spaces to d(w, 1), respectively. We then apply these characterizations for studying the relationship between the existence sets and one-complemented subspaces in d(w, 1). We show that a subspace of d(w, 1) is an existence set if and only if it is one-complemented.