Indices, convexity and concavity of Calderón-Lozanovskii spaces - Kamińska, A.; Maligranda, L.; Persson, L. E. (MATHEMATICA SCANDINAVICA, 2003)
In this article we discuss lattice convexity and concavity of Calderón-Lozanovskii space E_φ, generated by a quasi-Banach space E and an increasing Orlicz function φ. We give estimations of convexity and concavity indices of E_φ in terms of Matuszewska-Orlicz indices of φ as well as convexity and concavity indices of E. In the case when E_φ is a rearrangement invariant space we also provide some estimations of its Boyd indices. As corollaries we obtain some necessary and sufficient conditions for normability of E_φ, and conditions on its nontrivial type and cotype in the case when E_φ is a Banach space. We apply these results to Orlicz-Lorentz spaces receiving estimations, and in some cases the exact values of their convexity, concavity and Boyd indices.