GEOMETRIC-PROPERTIES OF SYMMETRICAL SPACES WITH APPLICATIONS TO ORLICZ-LORENTZ SPACES

We deal with the basic convexity properties -rotundity, and uniform, l ocal uniform and full rotundity - for symmetric spaces. A characteriza tion of Orlicz-Lorentz spaces with the Kadec-Klee property for pointwi se convergence is given. These results are applied to obtain criteria of convexity properties for Orlicz-Lorentz sequence spaces, and some n ew proofs of the sufficiency part of criteria for rotundity and unifor m rotundity for Orlicz-Lorentz function spaces.