Extreme and smooth points in Lorentz and Marcinkiewicz spaces with applications to contractive projections (Q734582)

Extreme points and smooth points in the Lorentz sequence spaces \(d(w,1)\) and in Marcinkiewicz sequence spaces \(d_*(w,1)\) and \(d^*(w,1)\) (which are predual and dual spaces to \(d(w,1)\), respectively) are characterized. In the second part of the paper, applying the characterization of smooth points in \(d(w,1)\) and extreme points in its dual \(d^*(w,1)\), it is proved that a nonzero linear subspace \(V\) of \(d(w,1)\) is one-complemented whenever \(V\) is an existence set. In order to prove this interesting result some auxiliary results are established first.