On Lorentz spaces Γp,w

We study Lorentz spaces Gamma(p,w), where 0 < p < infinity, and w is a nonnegative measurable weight function. We first present some results concerning new formulas for the quasi-norm, duality, embeddings and Boyd indices. We then show that, whenever Gamma(p,w), does not coincide with L-1 + L-infinity, it contains an order isomorphic and complemented copy of l(p). We apply this result to determine criteria for order convexity and concavity as well as for lower and upper estimates. Finally, we characterize the type and cotype of Gamma(p,w).