Local uniform rotundity in Calderon-Lozanovskii spaces

We find criteria for local uniform rotundity of Calderon-Lozanovskii spaces solving problem XII from [8] and generalizing several theorems, which give only the sufficient (or necessity) conditions (see [18], cf. also [5]). In particular we obtain the respective criteria for Orlicz-Lorentz spaces which has been proved directly in [19] and [4].